when u hit the open note, is it in tune? if it is, then it's most likely the intonation... here's a video on how to check and fix the intonation...
YouTube - Guitar Intonation Tutorial from HowAudio.com and Synthesis.n
Supposedly, it should be a B on your 19th? This is my take.
17th A
18th A#
19th B
20th C
But skips to C?
Fret is very worn on B. When you fret down, the string touches 20th fret and produces that note instead of a B (19th).
Try tightening your tension and raising your action. So it 'elevates' higher.
Might be cause of very low action, with very worn out frets. Don't know, could be :S
Sorry if this wasn't useful.
I'm a newbie! :S