It's not smoothness that's the problem, it's that it leads them behind, instead of leading them ahead.

The original JJ2 camera system is smooth, stays still enough when it needs to be and leads the player ahead. That's what makes it so great.

There's actually an article which helps explain how it works. In relatively simple terms though, the camera budges to the direction to where the player is going, which offsets the sprite a little. It is also stronger the faster they are going. When the player reaches a corner of the level, it stops (for example, if they reach the very top position of the level, it stops moving above). When they hit a wall horizontally and not jump, the camera slowly adjusts to the center. Setting to a smaller resolution demonstrates this more clearly.

As for missing animations, there's no spawn/consume animation (its the same). It's to do with getting pickups and respawning. Also not really an animation, but enemies/bosses appear to not blink white when they are hit. Which I think is important, since it shows they took the hit. The spinning sprite for going up from a spring/tube is also missing.

Something I also noticed odd about the physics is that you don't go up after buttstomping an enemy. Going up with that does have some utility. Best case scenario though would be to let the player go up after only if they hold jump. That makes it more versatile and flow better if they want to go down. Also, can you keep jumping if you hold on jump? Especially on one-ways.

Anyway..good luck. ;p