The length should be approximately 10 pages. This is only a rough guideline. However if your paper is a lot shorter than this then you might consider adding more explanations and examples to help the reader understand your topic. If your paper is n pages where n>10, then you have gone above and beyond the call of duty, and your instructor reserves the right to select n-10 pages to not read.
There must be some proof of something. A survey of interesting facts with no justification is not acceptable. It is however OK to omit some proofs of plausible technical facts. In any case, you want the reader to understand something, and you can decide which are the most salient points to explain.
When you omit details, you should give specific references (including pages or theorem numbers) to where these details may be found.
If your paper depends on advanced material which is well beyond or outside of what we did in this course, then your paper should include a crash course (with specific references) on the relevant prerequisites; otherwise there is a good chance that your instructor will be unable to understand your paper.
The topic should not be excessively broad. It is usually better to understand half as much material twice as well. Remember that "God is in the details."
Examples are good. Examples provide reassurance that we know what we are talking about. As Feynman said (in reference to useless physical theories, and I paraphrase), "if you can't compute examples, then you don't understand anything."
There should be an abstract. This is a paragraph at the beginning of your paper which summarizes what your paper does, and hopefully will motivate the reader to persevere through the paper.
Organization is not so critical in a short paper, but in general, at any given time the reader should know where they are, where they are going, and where the most interesting part is.
You should consider your audience to be the fellow students in your class. Your goal should be to teach them something. Anything which helps your audience understand mathematics is good.
Don't waste time correcting grammar and spelling mistakes. But do point out mathematically significant typos such as incorrect subscripts etc.
You should question things that are mathematically wrong or that don't make sense. Sometimes there are lots of these.
If you are having a hard time understanding the paper despite making a reasonable effort to do so, then you should complain, and beseech the author to include more explanation and examples.
You might not have time to digest the entire paper. But you should be sure to give some substantial feedback.
Of course you are welcome to change other things as well. Often, after putting a paper aside for a while, you will gain a fresh perspective and see many things that can be improved.