I think it just depends on the individual test. I've used expired $ store tests and Answer tests and they've always been accurate, but when I got pg. this time I had a CBE digital left over from DD (which showed "Pregnant" at 10 DPO with her) and it said "Not Pregnant" after multiple BFP's, so while I can't say it's because it was expired (by only a month!), it wasn't accurate, while with DD it was.
My guess would be anyway that you would be more likely to get a false negative than a false positive from an expired test. I just used a test that expired in August (not TTC, we plan to in the spring/summer but we both have the baby bug so we tend to get careless about birth control - I use FAM). Anyway, mine was negative, and that was correct as my temp dropped this morning (and yes, I am a bit sad about it, I think we need to move up our TTC date).