I think the # 1 area in which he may be behind his new classmates is writing. I would probably have him do bits of handwriting practice over the summer.
Also, if your child's kindergarten classroom schedule / structure will be markedly different from second grade (for example if he's in a half-day K), educate yourself and him about the changes, and think about asking for him to sit in with the graduating 1st class for a day or two if possible.
Another idea is to make sure you know what, if anything, the graduating first graders are expected to do over the summer; for example, they may be expected to do a summer reading plan. If there is summer work assigned, you may be able to have your son knock it out in a very short time, and he may feel less out of place if he has all of his ducks in a row.
You will of course have lots of conversations with your little one about the skip. Begin thinking about ways to prepare him and yourself if you encounter curious questions from kids and adults about the skip. I've already encountered some borderline-pushy parents, which was uncomfortable (thankfully they were in the grade our son is leaving).
I'm doing this for the first time, too, so take all my advice with a grain of salt.
