Q:

Is drinking water containing dirt harmful?

I noticed that if I collect water from a stream dense of small debris/thin mud, if I keep the water bottle close to the surface, while it takes a longer time to fill the bottle, the water is cleaner there.
In that occasion, the water was not that muddy, but it was muddy enough not to look clear - it had a very light brownish colour - and to taste "groundy" as well, despite my care in collecting it on the top of the small stream (which made a difference).
I boiled it; for quite some time (one good minute of hard boiling), so I assume it was very safe from a bacteriological point of view.
I am wondering though: there may be any health dangers caused by drinking all that tiny debris?
And, unhealthy or safe, it still tasted bad. Are there any - possibly simple and lightweight - ways to filter that? 
Like, may a coffee filter help? Or, what could/should be used, assuming that the water contains no dangerous chemicals and that the biological dangers are removed by boiling?
Please notice that this is not a generic question about water purification but it's very specific to debris and to lightweight backpacking.

A:

The terms to google on seem to be "turbidity," "total suspended solids," and "total dissolved solids." TSS refers to solids that can be eliminated by a filter, and TDS to solids that are in particles so small that they get through a filter. High TSS seems to be harmful to fish because it indirectly reduces the amount of oxygen: https://www.ndhealth.gov/WQ/SW/Z6_WQ_Standards/WQ_TSS.htm.  (Note that on 12/1/18 that link is not accessible.) 
Re safety for human drinking:

Turbidity itself is not a major health concern, but high turbidity can interfere with disinfection and provide a medium for microbial growth. It also may indicate the presence of microbes[...]

-- http://www.water-research.net/index.php/stream-water-quality-importance-of-total-suspended-solids-turbidity

High TSS in a water body can often mean higher concentrations of bacteria, nutrients, pesticides, and metals in the water. These pollutants may attach to sediment particles on the land and be carried into water bodies with storm water. In the water, the pollutants may be released from the sediment or travel farther downstream [...]

-- http://bcn.boulder.co.us/basin/data/NEW/info/TSS.html

High TDS concentrations can produce laxative effects and can give an unpleasant mineral taste to water.

-- http://bcn.boulder.co.us/basin/data/NEW/info/TSS.html
It sounds like drinking water with dirt in it is not usually a problem in and of itself, but may be correlated with the presence of disease-causing organisms or nasty stuff like pesticides and fertilizers. Of course if the alternative is to get seriously dehydrated, you're going to have to take your chances by drinking the water.

A:

Short answer, it depends.
As with all fresh water sources the  the important thing to notice is the context in which the water is in. I.e. where has the dirt come from? Where has the water come from?
Couple of points that affect this:

What is the dirt? Inert clay or run off from a sewer?
What type of terrain are you in? Low agriculture, mountain terrain or a heavily populated city?
What's above the water source? Does this water come from a natural mountain spring or a reservoir or lake.

Dirt, does not mean contaminated (just like clear water does not mean clean). The dirt could be very good for you (some minerals in suspension are actually beneficial)! or it could be very bad. It all depends on the context of where the dirt has come from and what it has been exposed to.
Everything in this question (Do you need to purify all mountain water
   sources) is relevant here. The fact that the water contains some particles in suspension is almost irrelevant. 
Boiling
Boiling will kill micro-organism contaminants, but not all, this is not a panacea. Lead and other heavy metals are not removed by boiling

A:

To add to Liam's answer, it depends what minerals/chemicals are in the water. Many of these are harmless (e.g. peat or clay), but other can be dangerous. In general, mineral contamination is not effected by boiling. Some chemical impurities can be removed by filtering, but most filters are primarily designed for removing microbes and will be of limited use for removing chemical contamination. There are lots of filters available (e.g. these or this). 
Most filters are not effective for chemical contamination as most of the chemicals are small single molecules and/or soluble in water, where as filters designed to remove bacteria have a pore size ~2um. To somewhat effectively remove chemical impurities a carbon filter can be used. Some ceramic pumps have a carbon filter built in. It should be noted that carbon filters clog up and need to be replaced or will stop working effectively.
Depending on your location mineral contamination is not likely to be an issue. It is mostly a concern in areas where there has been significant mining, industrial or agricultural activity, although does occur naturally in some areas. Some chemical contaminates to be aware of are:
Heavy metals: e.g. lead, mercury, arsenic. Are not normally a concern for surface water but if mining or industrial pollution has occurred in the area the wash out may contain high levels heavy metals. Severe exposure can cause vomiting, nausea and diarrhea. Longer term exposure can also lead to many unpleasant illnesses.
Pesticides etc.: Mainly occur as run off from agriculture can also get organic chemicals in mine run off. Can cause liver and kidney problems, primarily after long term exposure.
Uranium: Occurs naturally in some areas, but is more a concern where mining has effected the water supply. Primary health risk is from long term exposure.
Hydrogen sulphide Occurs naturally in some areas and can also be introduced by sewage water. Has a notable rotten egg smell. Drinking such water can cause stomach cramps and diarrhea.
Iron and copper Can occur naturally or from mine run-off. results in foul tasting water. In high concentrations they have been linked to liver failure but are not poisonous at low concentrations. 

