I haven't really pursued the highpoints, but I have Dominican Republic, Guatamala, El Salvador, Honduras, Costa Rica, Guyana (I think?), almost Ecudador (the highest mountain has more than one point on its crater rim), Australia and Singapore. I don't think Hong Kong can be counted any more (since it's been turned over to China). Others tried: I would have had Spain if it weren't for red tape near the summit and we failed on Russia due to a bad storm.
North Korea ain't happening anytime soon, that's for sure.
Since the peak is on the border of China and you are allowed to climb it from the Chinese side, it shouldn't be too hard to get that one.
I believe Burma's high point (somewhere north of 19,000 feet!!) may also be unclimbed and the government there, last I saw, wasn't allowing people to try.
It's been climbed once. It was a very difficult ascent and the approach through the jungle was horrendous.
Saudi Arabia may be another tough one, mainly because of access issues.
But I'll bet most of the rest are more accessible.
Most perhaps, but some that wouldn't be:
The highest mountain in Bhutan hasn't been climbed yet and would be a tough one. Pakistan has K2 and India Kanchenjunga which are tough ones. If I remember right either Suriname or Fench Guiana is very difficult, but I don't remember which one. I think Algeria's is really difficult as well (technical). The high point in French Polynesia and some of the other island countries are quite difficult as well. Chad's highest peak is a non-technical climb, but really hard to get to. Some of the highpoints in the Middle East are off limits due to communications and military installations. Afganistan's high point is considered to be one of the easiest 7000 peaks, but is probably off limits. Not sure about Iraq's.
What are some of the easier national ones, anyway?
In addition to the ones already mentioned:
Spain's is both hard and easy. It's easy because a cable car goes very high on the mountain, but hard because you must have a permit to get to the very highest point. El Salvador's has a road to the top, but you can hike a trail up too. Same with Panama's. Australia's is pretty easy. Singapore's is easy, but hot and sweaty 365 days a year.
I'm slow and fat. Unfortunately, those are my good qualities.