I hate statement modifiers. All except "for". Anyway, whenever in doubt place parens and/or check:

$ perl -MO=Deparse -e'push @badVals, $val && next if isBad($val);'
push @badVals, $val && next if isBad($val);
-e syntax OK
$ perl -MO=Deparse -e'(push @badVals, $val && next) if isBad($val);'
push @badVals, $val && next if isBad($val);
-e syntax OK
$ perl -MO=Deparse -e'push @badVals, ($val && next) if isBad($val);'
push @badVals, $val && next if isBad($val);
-e syntax OK
$
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Note that all parse the same, and thus probably do not do what you expected it to do. Compare to:

$ perl -MO=Deparse -e'(push @badVals, $val) && next if isBad($val);'
push @badVals, $val and next if isBad($val);
-e syntax OK
$ perl -MO=Deparse,-p -e'push @badVals, $val && next if isBad($val);'
(isBad($val) and push(@badVals, ($val && next)));
-e syntax OK
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update: added -p example after kcott's post.