The following source causes the "EXERCSISES" head in the theorem-like environment to be overwritten with the 1st item of the enumerated list inside:
\documentclass{article}
\usepackage{amsthm}
\usepackage{thmtools}
\usepackage{enumitem}
\declaretheoremstyle[
headfont=\bfseries,%
headpunct={\vspace{\topsep}\newline},
numbered=no,
spaceabove=3\topsep,
postheadspace=0 pt ]{exercs}
\declaretheorem[name=EXERCISES,style=exercs]{problems}
\newlist{problemsenum}{enumerate}{3}
\setlist[problemsenum,1]{%
label=\arabic*.,
before=\leavevmode \vspace{-\dimexpr\baselineskip+\topsep\relax}
}
\usepackage{showkeys}
\begin{document}
\begin{problems}
\label{myproblems}
\begin{problemsenum}
\item Do this one first.
\item Solve this next.
\end{problemsenum}
\end{problems}
\end{document}
Commenting out the \usepackage{showkeys} or omitting the \label prevents the overwriting:
Is there some way to prevent the overwriting even with showkeys loaded and with the \label still included?
One way to prevent the overwriting when showkeys is not loaded is simply to remove the newline between \begin{problems} and the \label command:
\begin{problems}%
\label{my problems}
However, even with that change, once showkeys is loaded the overwriting persists. Hence a more robust workaround would be desirable.
Note: The seemingly convoluted definition of the problemsenum environment is needed in order to be able to create cross-references to individual items in the problemsenum environment, with \cref, even though the theorem-like environment is unnumbered. (See How use cleveref to get theorem-like name and list item number? and How change vertical space after head in theorem-like environment .)


\label? There isn't anything there to refer to, is there? – cfr Sep 22 '16 at 22:21showkeysoperates in horizontal mode, I think. However, you have put TeX in vertical mode, also I think. Hence, no adjustment is done. – cfr Sep 22 '16 at 22:41\hskip 0ptafter\label. But you would be better advised to heed the recommendations provided in response to your earlier questions, I think. – cfr Sep 22 '16 at 22:43\usepackage[left]{showlabels}instead of\usepackage{showkeys}. Theshowlabelspackage is usually more robust thanshowkeys. David will appreciate. – egreg Sep 22 '16 at 22:52\leavevmode \vspaceis a very weird construct, it forces the space into a vadjust node so that it is inserted after the paragraph has been broken into lines, after the first line of the paragraph. – David Carlisle Sep 23 '16 at 00:15problemsenvironment. (All problems are numbered consecutively within the chapter, not the section; with a counter\problemnumberreinitialized at the start of each chapter, and added keysafter=\stepcounter{problemsenumi}\setcounter{problemnumber}{\value{problemsenumi}}andstart=\value{problem number}in the\setlistfor\problemsenum, everything else takes care of allowing cross-references to individual problems withcleveref. – murray Sep 23 '16 at 19:44show labelsinstead ofshowkeys. That allows me better control over the labels, too, e.g., to put them in the inner (in my situation, wider) margin and to print them in a smaller size. – murray Sep 23 '16 at 20:16