Typesetting issues
Nesting of sectioning commands
It is recommended to use proper nesting of \section-like commands, for example you should not follow up a \section by a \subsubsection, but by a \subsection. This inspections includes two quickfixes, to change the sectioning command to the right one (change \subsubsection to \subsection in this example) and to add the missing sectioning command (\subsection in this case).
Collapse cite commands
\cite{knuth1990}\cite{goossens1993} should be replaced with \cite{knuth1990,goossens1993}
En dash in number ranges
Instead of typing 0-9 for a number range, use 0--9 to typeset the right dash.
Use of . instead of \cdot
When multiplying numbers, use \cdot instead of ..
Use of x instead of \times
When multiplying numbers, use 2 \times 4 instead of 2x4.
Vertically uncentered colon
Instead of :=, use \coloneqq for better vertical centering of the colon.
Insert \qedhere in trailing displaymath environment
If you end a proof environment with a displaymath environment, the qed symbol will appear after the displaymath which is one line too low, so you should use \qedhere in the displaymath environment to fix that.
Dotless versions of i and j must be used with diacritics
When you use diacritics like ^ on an i or j, you should use the dotless version for better readability. For example, instead of ^i write ^{\i}.
Enclose high commands with \leftX..\rightX
Expressions which take up more vertical line space, should also be enclosed with larger parentheses. For example, instead of (\frac 1 2) write \left(\frac 1 2\right).
Citations must be placed before interpunction
Use Sentence~\cite{knuth1990}. and not Sentence.~\cite{knuth1990}