How to review bogus science without hurting feelings? I've been forwarded a four-page outline of some sort of "theory of everything" whose ambition is to explain just about everything in the universe in terms of particles oscillating in and out of some kind of hidden anti-universe. I've been asked to give my opinion on the theory.

It has all the hallmarks of bogus science written by someone with only the vaguest notions of quantum physics and cosmology (no equations, electrons being defined as the antiparticles of protons, cute drawings). Perhaps more telling is that most of the ideas are unfalsifiable, in the sense that I couldn't think of an experiment that would prove or disprove any of it.

I'd like to give my frank opinion about it without hurting the person's feelings. How should I go about it?
So, I see that you're conflicted by the desire to give your honest opinion and your desire to be nice. While some say you should let go of the desire to be nice, I think in this case it might be more productive to first look at how you can be nice. But first, let me briefly talk about 'cranks':

What are cranks?

The following quote from Nature is prominently placed on the Wikipedia article on cranks:


  A crank is defined as a man who cannot be turned.


Less cryptically, an important property of crank is the unwillingness to change their line of thought or accept being wrong (they likely admit to make 'unimportant' mistakes and will immediately explain what they 'actually' meant). This will become a very useful definition. Suppose for the moment that exactly one of the following is true about the motivation of your correspondent:


"I have a brilliant idea about the universe and by showing this to an expert, I'll get the recognition I deserve."
"I don't know much about Physics, but I think this is a good theory and want to know what the experts think."


Note that person 1 is a crank, for when you tell (1) that this idea is 'bogus', the reaction will be likely hostile, as (1) will refuse to be 'turned'. Any conversation with (1) is a waste time. If your know for certain that you're dealing with person 1, ignoring, aborting and running away in the most polite way possible is recommended. However, as you desire to be kind to your correpondent, I doubt you are certain that you're dealing with person 1. (Also, assuming 1-ness might be dangerous. Applying Hanlon's razor seems like a good idea.)

How to be nice to person 2

Now, is person 2 a crank? (2) could be a crank, but not necessarily. Perhaps (2) is simply a layman who always had an interest in physics, but never had (or took) the chance to pursue this interest with proper study and thinks this is how physics can be done. 

For person 2, I think the best way to be nice is to not give your opinion on the  work, other than that it simply is hard for you to judge (2)'s actual ideas as they are very non-standardly presented. (This can be a lie. But I think it is a very useful lie.) It is important that you add the advice that if (2) has an interest in physics, (2) should learn more about physics so that (2) can properly present the theory. It is good to add some explicit method for (2) to do this, such as some introductory books, courses or videos. 

In the best case, (2) will start learning things and eventually will realize that his theory is 'bogus' by themselves! In the worst case, (2) will show the inability to 'turned'. But thereby, (2) reveals to be (1) all along and you can therefore safely abort communications with your correspondent. 

Conclusion

I think it is good you ask this question, because I believe there is a true dilemma here. You must choose at most one of:


Share your (brutally) honest opinion with your correspondent.
Help your correspondent by gently directing them to the path of learning.


Any combination of the two will likely act as a discouragement for your correspondent from attempting to learn, for your correspondents idea that they might be able to do some physics is likely crushed by the weight of an experts opinion.