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On cheaper instruments the 1st fret on the guitar body seems to be the one that causes most of the trouble. A good 24″ straight edge is a good way to check for overall fret issues if you have the neck adjustments perfectly straight. This gives you an over idea of where problems can exist. Then your fret rocker can zero in on which frets are causing the most problems.
Like you said if you raise the bridge saddle it can overcome those issues but it is harder to fret. For every 16th of an inch that you raise the saddle will raise the string action, at the 12th fret a 32nd of an inch or which ever amount you raise the saddle height equals half of that height higher at the 12th fret.
Also if the frets weren’t dressed properly to begin with you can have one part of the fret too high and all of the other string positions on that fret perfect.