Ex-husband wants full custody of my boys....grounds?

I've been divorced for about a year. I am the primary custodian of our boys, ages 3 and 5. My ex-husband is a difficult man to deal with, but that's a different story. He remarried this past June and he and his new wife live in a nice home and take good care of my boys when they are at his house (he has them 10 nights a month, I have them the remaining 20). I have no qualms with the way they are treated at his home. My only issues with him have been personal. He called me today and said that he didn't think I was taking good enough care of the boys and wants to take them from me...for the following reasons: They come to his house with mismatched socks, they wear hand-me-downs, and I cut their hair at home instead of taking them to a barber. There was also a day (my scariest one ever), when the sitter I entrusted with my boys while I went to the grocery lost sight of my three year old and he wandered in to the street. Thank God he was OK. Plus, he had to buy my youngest new shoes a few weeks ago because I couldn't afford to buy new ones at that time, even though he pays me child support (his words, not mine). Now understand that every cent he gives me plus some I pay out in child care while I'm working full-time. I don't have a lot of spare money. I do my best. I don't always give my kids the amount of attention I would like to, and it shows in their behavior sometimes. I have my not-so-proud moments when I yell at them for jumping on my furniture or other things that little ones do. I'm not perfect. But I truly love my children. They are not neglected in any way. They have a roof over their heads, warm beds, food in their bellies, clean clothes on their backs, and a plethora of love and hugs and kisses from their mommy. I think I'm doing the best I can being a working single mother of two young children...apparently he disagrees. Does he have grounds for full custody?