PIC16 10hz timer with timer1 and 1Mhz clock
Instead of using the 16-bit timer 1, which requires you to reload the value in code, use the 8-bit timer 2, which has a preset register PR2.  Load PR2 with 250, with a prescaler value of 1:1.  It will then interrupt every 1 ms and reload it self automatically so no latency problems.

The inside your interrupt, just increment a single byte counter.  In your base routine, use a while loop and test whenever the counter is equal to 100 (i.e. 1/10 of a second has elapsed).  Then reset the counter and do your clock/led updating and resetting there in the base level, not in your interrupt routine.