I have drawings with assigned plot styles for certain lines, set up in Plot Style Table Editor. Here’s my issue. The plotted line weights for these lines are 1.2 mm .I had the line end style set as Square. The lines were protruding past the object or line they were intersecting with. I changed the line end Style to Butt hoping that it would correct the problem, but no luck.Any suggestions?

If all lines are the same weight you should be ok. If you have a thicker line runing into a thiner one, this happens.
 
Also, click on the line that's acting up & see if the griping point is going past the line you're intersecting too. I'll try to quickly lay lines down & my o-snap will grab something i didn't want it to if you have objects close together.
 
Zoom in, cause it's hard to notice on large drawings sometimes. It also helps me to highlight everything in the area just to see grips of things I may not have caught while not selected.
 
I'm sure you'll kick yourself when you find out what it is.