If it makes you feel any better (which it may not :) my son is 4 1/2, and he is exactly the same way. His vocabulary is awesome, his problem solving skills are terrific, but like your son, he doesn't always count to 10 in order, without skipping numbers, he sings his abc's, sort of, also sometimes skipping or mixing them up, and he is just starting to be able to write his name by copying it if I write it first, and even then, it's very rudimentary. He was never one to learn songs and sing them much, and he is a very typical little boy - very active, rarely sits still, and even when talking or doing something, is always moving. However, he loves to read (i.e. look at his books) and be read to. And his memory for events and things is fantastic. He will remember details of situations, things he saw, or said, or did, or things I said or did, with way more detail than I remember.
At times, I get a little concerned about his "academic" progress, but I quickly talk myself down. He is in his second year of preschool also (2 half days/wk last year, and 3 half days/wk this year.) He is absolutely fine. He will get things in his time. We are taking the NO PRESSURE route for now. He is 4, for Pete's sake. I don't want him turned off from formal learning before he's even in school! He has a ton of exposure to learning opportunities, both through books/computer, as well as experiential, and he gets a ton of individual attention. He'll get these things when he is mature enough. I refuse to stress about it or compare him to other kids who have been singing their abc's since they were one. Every kid has strengths and some kids get those things earlier. My son learned to walk at 8 months. He is extremely physically capable. He is strong and agile. And he is extremely sensitive, emotionally responsive, and loving. And that is fine with me. As long as he is on the curve, or if he's struggling, that I'm doing what I can to help him, then that's good enough for me.
I guess my point in saying all that is that you are not alone, and you son is probably a lot like many little boys his age. Don't stress too much about it yet. Let him grow up a little. If his teachers say he's ok, then for now, let that be enough. Keep your eyes and ears open, and if at some point, he is actually struggling, you'll know.
Blessings to you and your perfectly wonderful little boy.