user18: I've been struggling with this one for quite a while now. The fourth foundation of mindfulness is called 'dhammānupassana' - vision in regards to the dhammas. The old translation I was given when I started meditating was "mind objects", which I'm pretty sure is not at all correct in this context, since it doesn't get at the distinction between the fourth set and the first three.
The phrase "mind object" is a translation of "dhammarammana". According to Nina Van Gorkom, 

Dhammarammana comprises all objects which are not included in the first five classes. These can be experienced only through the mind-door.
http://www.budsas.org/ebud/nina-abhidhamma/nina-abhi-16.htm

So, "mind object" is a specific subset of reality in a specific context. The first five indriya and the first three elements that comprise rupakkhandha are not a part of this subset, and yet they appear in the section on dhammanupassana.
The commentary says relating the the fourth satipatthana, 

and now in order to speak of even the laying hold of the aggregates of perception and formations, he said "And, how, o bhikkhus," and so forth." 

So the emphasis is supposed to be on these two aggregates (even though the five aggregates themselves are under this heading).
In Thai, the meaning is given as "that which holds (dhareti) the meditator from falling into evil", which is a definition of the truths (dhammas) taught by the Buddha. That seems appropriate, but it is still curious that there are only a limited number of subsets of the Buddha's teaching in the satipaṭṭhāna sutta, certainly not all of the Buddha's teaching.
Does anyone have a proper explanation as to why the fourth set is called "dhammas"?

user16297: 
Does anyone have a proper explanation as to why the fourth set is called "dhammas"?

Because the 4th category is not about dhamma (mental qualities or phenomena), it's 
☸Dhamma-[teaching that leads directly to nirvana].
http://notesonthedhamma.blogspot.com/2019/07/proof-dharma-is-buddhas-teaching-not.html
The standard Theravada interpretation of the cryptic formula in 4sp satipatthana, is that one focuses on one of the frames to the exclusion of the other 3. But that's not the real purpose. The real meaning, is that one  should see "body as body [as it actually is]".
http://notesonthedhamma.blogspot.com/2019/05/the-real-meaning-of-cryptic-formula-in.html
For ☸Dhamma, the meaning of seeing ☸Dhamma as ☸Dhamma as it actually is, is very similar in meaning to the meaning of ☸Dhamma-anu-dhamma☸
{the practice of} dhamma/Dhamma that accords with {the Buddha's} ☸Dhamma.
http://lucid24.org/tped/d/dhamma/index.html
EA, the MN 10  (satipatthana sutta) parallel in Chinese Agama, supports my interpretation
Or at the very least, has an idea much closer to mine, than to Theravada.
It looks like they're interpretation is that you take any dhamma [thing, quality, phenomena], and put it through a thorough ☸Dhamma investigation, after attaining 4 jhanas via 7sb.
(chinese and english translation of passage here):
https://notesonthedhamma.blogspot.com/2019/07/what-is-dhamma-category-in-4sp.html
my response to one of the comments below:
in DN 22 though, the 4 noble truths and noble eightfold path description under Dhammaanupassana are just cut and paste jobs from other fundamental suttas defining what those factors are. Unlike the EA parallel where Dhamma anupassana is described where you're activing USING a Dhamma-teaching framework to analyze the phenomena. DN 22 maybe implies that, but the Theravada model is so massive and convoluted you can't tell for sure. In EA, for sure that's what they're doing. The problem is if you take DN 22 as viewing dhamma-phenomena viewed through Dhamma-teaching framework, then how do you approach the other 3 satipatthana where that wouldn't work? It doesn't say kaya-Dhamma-anupassi, vedana-dhamma-anupassa, etc...

user145: I think the following perspective on all four satipatthanas will help in understanding the  meaning of the fourth one. The four satipatthanas are supposed to counter the four vipallasas (perversions) which are: permanence, happiness, self, and beauty. So, mindfulness of the body counters the beauty perversion; mindfulness of feelings (and the fact that all vedanas are included in dukkha) counters the happiness perversion; mindfulness of mind (which is anicca) counters the permanence perversion; and, finally, mindfulness of the dhammas counters the self (atta) perversion. Thus, one reviews dhammas to realize anatta. To view four perversions would be inappropriate attention (ayoniso-manasikara), but the four satipatthanas, would be training in appropriate attention (yoniso-manasikara).
So, overall, I think the meaning of dhamma in this context is exactly what they are: analytical properties of experience, ultimate phenomena, and everything else that apply to dhammas (mind objects, matikas, dhamma lists, etc).

18: <p>I've been struggling with this one for quite a while now. The fourth foundation of mindfulness is called 'dhammānupassana' - vision in regards to the dhammas. The old translation I was given when I started meditating was "mind objects", which I'm pretty sure is not at all correct in this context, since it doesn't get at the distinction between the fourth set and the first three.</p>

<p>The phrase "mind object" is a translation of "dhammarammana". According to Nina Van Gorkom, </p>

<blockquote>
  <p>Dhammarammana comprises all objects which are not included in the first five classes. These can be experienced only through the mind-door.</p>
  
  <p><a href="http://www.budsas.org/ebud/nina-abhidhamma/nina-abhi-16.htm">http://www.budsas.org/ebud/nina-abhidhamma/nina-abhi-16.htm</a></p>
</blockquote>

<p>So, "mind object" is a specific subset of reality in a specific context. The first five indriya and the first three elements that comprise rupakkhandha are not a part of this subset, and yet they appear in the section on dhammanupassana.</p>

<p>The commentary says relating the the fourth satipatthana, </p>

<blockquote>
  <p>and now in order to speak of even the laying hold of the aggregates of perception and formations, he said "And, how, o bhikkhus," and so forth." </p>
</blockquote>

<p>So the emphasis is supposed to be on these two aggregates (even though the five aggregates themselves are under this heading).</p>

<p>In Thai, the meaning is given as "that which holds (dhareti) the meditator from falling into evil", which is a definition of the truths (dhammas) taught by the Buddha. That seems appropriate, but it is still curious that there are only a limited number of subsets of the Buddha's teaching in the satipaṭṭhāna sutta, certainly not all of the Buddha's teaching.</p>

<p>Does anyone have a proper explanation as to why the fourth set is called "dhammas"?</p>
 16297: <blockquote>
  <p>Does anyone have a proper explanation as to why the fourth set is called "dhammas"?</p>
</blockquote>

<p>Because the 4th category is not about dhamma (mental qualities or phenomena), it's 
☸Dhamma-[teaching that leads directly to nirvana].</p>

<p><a href="http://notesonthedhamma.blogspot.com/2019/07/proof-dharma-is-buddhas-teaching-not.html" rel="nofollow noreferrer">http://notesonthedhamma.blogspot.com/2019/07/proof-dharma-is-buddhas-teaching-not.html</a></p>

<p>The standard Theravada interpretation of the cryptic formula in 4sp satipatthana, is that one focuses on one of the frames to the exclusion of the other 3. But that's not the real purpose. The real meaning, is that one  should see "body as body [as it actually is]".
<a href="http://notesonthedhamma.blogspot.com/2019/05/the-real-meaning-of-cryptic-formula-in.html" rel="nofollow noreferrer">http://notesonthedhamma.blogspot.com/2019/05/the-real-meaning-of-cryptic-formula-in.html</a></p>

<p>For ☸Dhamma, the meaning of seeing ☸Dhamma as ☸Dhamma as it actually is, is very similar in meaning to the meaning of ☸Dhamma-anu-dhamma☸
{the practice of} dhamma/Dhamma that accords with {the Buddha's} ☸Dhamma.
<a href="http://lucid24.org/tped/d/dhamma/index.html" rel="nofollow noreferrer">http://lucid24.org/tped/d/dhamma/index.html</a></p>

<p><strong>EA, the MN 10  (satipatthana sutta) parallel in Chinese Agama, supports my interpretation</strong>
Or at the very least, has an idea much closer to mine, than to Theravada.
It looks like they're interpretation is that you take any dhamma [thing, quality, phenomena], and put it through a thorough ☸Dhamma investigation, after attaining 4 jhanas via 7sb.
(chinese and english translation of passage here):
<a href="https://notesonthedhamma.blogspot.com/2019/07/what-is-dhamma-category-in-4sp.html" rel="nofollow noreferrer">https://notesonthedhamma.blogspot.com/2019/07/what-is-dhamma-category-in-4sp.html</a></p>

<p><strong>my response to one of the comments below:</strong>
in DN 22 though, the 4 noble truths and noble eightfold path description under Dhammaanupassana are just cut and paste jobs from other fundamental suttas defining what those factors are. Unlike the EA parallel where Dhamma anupassana is described where you're activing USING a Dhamma-teaching framework to analyze the phenomena. DN 22 maybe implies that, but the Theravada model is so massive and convoluted you can't tell for sure. In EA, for sure that's what they're doing. The problem is if you take DN 22 as viewing dhamma-phenomena viewed through Dhamma-teaching framework, then how do you approach the other 3 satipatthana where that wouldn't work? It doesn't say kaya-Dhamma-anupassi, vedana-dhamma-anupassa, etc...</p>
 145: <p>I think the following perspective on all four <em>satipatthanas</em> will help in understanding the  meaning of the fourth one. The four <em>satipatthanas</em> are supposed to counter the four <em>vipallasas</em> (perversions) which are: <em>permanence, happiness, self</em>, and <em>beauty</em>. So, mindfulness of the body counters the <em>beauty</em> perversion; mindfulness of feelings (and the fact that all <em>vedanas</em> are included in <em>dukkha</em>) counters the <em>happiness</em> perversion; mindfulness of mind (which is <em>anicca</em>) counters the <em>permanence</em> perversion; and, finally, mindfulness of the <em>dhammas</em> counters the <em>self</em> (<em>atta</em>) perversion. Thus, one reviews <em>dhammas</em> to realize <em>anatta</em>. To view four perversions would be inappropriate attention (<em>ayoniso-manasikara</em>), but the four <em>satipatthanas</em>, would be training in <em>appropriate</em> attention (<em>yoniso-manasikara</em>).</p>

<p>So, overall, I think the meaning of <em>dhamma</em> in this context is exactly what they are: analytical properties of experience, ultimate phenomena, and everything else that apply to dhammas (mind objects, matikas, dhamma lists, etc).</p>
