I think I have accepted that my budgies are not going to be hand-tame - after talking it over with my vet, I got Robirda (a boy - the name stuck) a companion, Claudius, instead of trying to socialize him any more to me. Both are older rescues (one outdoors, one from someone on Craigslist). They've both been through quarantine and have a clean bill of health (well, Claudius had to have a Lupron shot for a benign testicular mass - but that's over and done with now!).
They're such good companions, their singing cheers up the whole house, I love talking to them and watching them play with their toys. I've got them in a triple-decker Prevue Hendrix flight cage, and we're building out a bigger aviary area where they can explore more outside of the cage.
However, they're just not hand-tame. Since I transitioned them to pellets (a whole other piece of drama - Robirda managed to starve himself into a vet visit + antibiotics the first time, but I followed Greg Burkett's seed-to-pellet advice the second time and was more successful) they'll both step onto my flat hand for millet, but Robirda in particular gets very scared and bitey at anything but a flat, food-covered hand. He was very sick when I found him and had a lot of frightening handling and syringe-medication before I could have a chance to tame him, so it makes sense.
Of course in a perfect world I'd like them to do step-up, be able to be weighed, maybe even be able to take treats from a syringe like I see bigger parrots do, etc. But in this world, where I love hanging out with them but am just not pushing them to have hand skills, what else do I need to keep an eye on? Of course I keep their cage clean, change their water, have 2 doors (one with an auto-close hinge and a latch) between them and other pets, etc. They're good at eating their vegetables, though they'd rather have lettuce than anything else and turn up their beaks if I overblanch the darker/healthier greens!
I guess I'm wondering if there are any specific things that I need to be mindful of with non-tame budgies who aren't being handled very much. I do keep an eye on them for lameness, puffiness, etc. because I know it's easier not to check on a bird you're not handling.
It sounds as if you are doing a very good job with your budgies.
Mine are not hand-tamed either. I ensure they have good food, lots of out-of-cage time and keep a close eye on their overall physical condition.
You are doing all of those things so keep up the good work!