Could be... but @1200 baud, you shouldn't have much problem.

However, could you also try few things
1. Make sure your circuit is properly filtered, no noise on your Vdd line (decoupling caps here and there)
2. Change SERIN/SEROUT for DEBUGIN/DEBUG
3. Try with HSERIN/HSEROUT with the proper DEFINEs.
Code:
DEFINE HSER_RCSTA 90h ' Enable serial port & continuous receive
DEFINE HSER_TXSTA 20h ' Enable transmit, BRGH = 0
DEFINE HSER_SPBRG 51  ' 1200 Baud @ 4MHz, 0.17%
DEFINE HSER_CLROERR 1 ' Clear overflow automatically