Hi

Looking at the circuit all looks OK for me. LSB's grounded on display, good !... For me I would have decoupled (0.1uf) around all the chips including the display. I also would have used a trimmer across 5v and 0v (5k) on the contrast (Pin 3)so as I could meddle !!

Nothing wrong in checking all connections are right way around on the board D4-D7 also RS and E, so easy to assume... "I know" I have been burned so many times.

Could be worth checking the Xtal.... Maybe just try switching to internal clock (4Megs), I have had strange things happen around crystal circuits and displays, Some of the EBay types certainly :-) .... Not just with PIC's but other Micros also.

One last thing make sure you protect your AC SSR outputs ... I love MOV's ...At least do fuse them. Good practice to fuse the the low voltage AC before the bridge also.

Hope some of this helps

Andy