Occasionally you may need to "squeeze" in a dimension and you may need to change its size to do so, the dimension overrides allow you to do this. To turn them off, in your Dimension style dialog box, just double click the style you were using, and AutoCAD will warn you: "Setting another style current will discard your style overrides." You just click Ok and you'll have them turned off.
Not sure what you mean about your angular units, is this in the units dialog box or is this in your dimension variables. If its the dimension variables, you may either causing an override, and then inadvertently turning them back off, or vice versa. If its the units dialog box, one of the biggest culprits I've found over the years have been lisp routines which needed system variables set to operate correctly and then either had an ungraceful exit, or the programmer didn't set them back - so you may check any lisp routines or even menu macros you may be using.
HTH
Todd
