The following common mistakes (LaTeX typos) should be taken care of while writing a research paper or an article in math.

1. Name of your latex file should not conflict with the name of a document class, a package or a latex engine, e.g. 'latex', 'article', 'beamer' etc.
2. Do not follow your style of formatting, always follow the standard or that is recommended by the document class.
3. Add ams packages in order: amsmath, amsthm, amssymb.
4. Do not use inline math for the purpose of styling words in italics, instead, use \it{} or \emph{}. To see the difference, see how awkward the output of $difficult$ looks like (see the 'ffi' part).
5. Use '\sup', '\inf', '\sin' instead of 'sup', 'inf', 'sin', and so on inside math environments. Function names having more than one character must be written in the roman style. For example, if you define a new function named 'deg', then use '\operatorname{deg}' wherever it is to be written, or define in preamble \DeclareMathOperator{\deg}{deg} and use \deg wherever needed (Before doing this, verify that the command \deg is not predefined).
6. Avoid the \displaystyle command in inline math, it causes unnecessary line spacing.
7. For the norm symbol, use \Vert \Vert instead of || || (see the gap between the pipes).
8. Do not manually write references; use MRef instead.
9.