Should I keep giving him the bennefit of the doubt?

My boyfriend is married (yes, I know, BLAH BLAH BLAH) but we have been seeing each other for over a year now. I love him and I know he loves me. He has a job that keeps him very busy on top of his obligations to his wife, parents, siblings, etc. He is constantly missing dates, times when we are supposed to get together and even forgot my birthday.

Reccently he disclosed that he had been lying to me about several things (including his name, where he lives, and where he works). In all fairness I had been lying about a lot of things as well and I came clean shortly after.

I have a difficult time discerning what is truth and what is a lie now. I used to trust everything he said but now there is always doubt. He didn't have to come clean, he could have continued to lie to me and I would have never known. Doesn't that have to count for something?

Everytime he misses something or can't make it to something my mind automatically goes to the worse case scenerio. Is he seeing another girl? Is he lying and really not doing what he says he is? Does he just not want to see me?

I don't want to be a total nag, so should I question him more often or just believe it until I have a reason not to?

Thank you for reading and your responses!