With the bugs fixed, DKJr has the potential for improvement, but there are some design concerns.
The first priority imho is that a "DKJr Remix" should not pivot to be more like Donkey Kong. DKJr is its own separate entity, and the things that make DKJr fun should not necessarily be the same things that make DK fun. With that in mind, some core principles still apply:
1.] Burning the clock out for points is boring no matter what game it is (think leeching Kong's leg on the rivet stage, or leeching off the spring on L=02 and L=03). There are some examples in DKJr as well, such as point pressing on the jungle/vine board and point pressing in the hideout. I don't agree that the timer should be limited. I think there should be more randomness thrown into these leeching elements to make the risk+reward factor much higher, similar to DK barrel board grouping. DKJr lacks this kind of depth, and adding this kind of player choice is what it desperately needs. DKJr has a reputation for being "pattern-based", and while some of that is good, other parts are not so good.
2.] With the exception of bonus stages, there should never ever be an instance of a DK Remix "crack corner" similar to the rivet board (especially on 1-2). This is too random to be taken seriously in competition, even more random than the standard DK 1-2. If you're shooting for a great score and the fireballs don't cooperate perfectly, it's an insta-reset over the course of multiple screens. If this were to be on a bonus stage, I would strongly recommend "capping out" the bonus stage. For example: you have a bucket of 8000 points to fill, if you fill them in a crack corner scenario more power to you.
3.] There may be some differing opinions on this, but blank level labels are jarring. Having a L=A, L=B, and L=C is really cool and part of the JR charm that should definitely remain, but from a spectator perspective seeing nothing for the level indicator makes a game more difficult to follow.
4.] The point spread in DKJr needs to have a serious evaluation if we're talking about design. In DK, you have a tight but elegant point spread representing every rung of the ladder, meaning a 850k kill screen, 900k clean-up phase, 1.02m, 1.07m, 1.1m, 1.13m, 1.15m, 1.2m+. These are zones that gameplay will fall into when playing to a certain formula if that formula is perfectly executed, no matter what happens. DKJr has some zones of its own, but they're much more erratic and there are fewer of them. There are fewer rungs on the ladder because the skill ceiling is not as high as DK, and that's a serious problem.
That's really all I can think of. The most glaring issue with DKJr is most of the point pressing is boring as fuck. There is very little randomness to it... it's just tedium. It's easy to learn. It's easy to master. With DK, grouping can take literally months and months to learn because of all the weird edge cases you'll find -- all of which are survivable... that is very important. It definitely wasn't designed that way, it's just a beautiful accident. With the exception of screens that are more cerebral (the chain board), the skill ceiling for the game is much lower than DK.