Listed here are the frequent tips when I proofread papers from master or phd students. They are numbered for convenient indexing. When I see a problem, I marked its corresponding number on the paper that I proofread to save my time. The correctness is not guaranteed. 

[1]. The usage of a hypen, en-dash, and em-dash

They are different, but often abused by fresh authors. In "trade-off", "-" is a hyphen. In "pp. 134–150", "–" is an en-dash, indicateing a pertinent range. While an em-dash is graphically denoted as "—", it is called a punctuation, used in a sentence. 

In LaTex, "-" generates a hyphen, "--" gives an en-dash, and "---" yeilds an em-dash.

[2] A comma cannot connect two sentences

[W] Samy is good at math, Sana is good at English.

[C] Smay is good at math and Sana is good at English.

[C] Samy is good at math, Sana is good at English, and Grace does not like Latin.

[3] The usage of that

[W] Assume p is an integer.

[C] Assume that p is an integer.

[C] Assuming that p is an integer, 2p+q must be a real number.

[W] We conclude p is an integer.

[C] We conclude that p is an integer.