Weierstrass Thm: Continuous Fn Attaining Extrema on Compact Domain $u:\mathbb{R^L}\rightarrow\mathbb{R}$ This is just semantics, but MWG doesn't use the Weierstrass Theorem in its Math Appendix when using the fact that a continuous function always has a max value on any compact set.

Some books appeal directly to the Weierstrass Theorm.

Is there a right or wrong answer to this? Or is it more just, like I said, semantics?
The Weierstrass Extreme Value Theorem guarantees this. However, it's used so frequently that economists take it for granted or omit it in graduate courses and research papers. MWG is a maturity book. Part of mathematical maturity is being able to fill in the details for a proof.