1) Local axes. MMD's local axes relate only to the use of the rotation rollers-- not for things like IK angle limits, which always use global axes. You can get around this by setting up an IK bone in the global axes and then initializing it into different axes by placing an IK target someplace else, or by appending from another IK bone doing the same thing (for initializing complex local axes). This often means transforming a model into a weird default position, such that the IK drags the model into the right position. Initializing angle from other IK bones runs into weird bugs and requires more levels of deformation tier than you'd expect, but once it works, it stays working.
2) Stacked constraints. Use another layer of bones-- another bone in the same location, parented in a chain.
3) Damped track. Single most useful constraint. Use a single bone IK chain. A warning that applies whenever using MMD's IK bones: they fail in circumstances where Blender's IK bones don't. In particular, they fail when forbidden to rotate in at least one axis and asked to point directly toward or away from their default position. Increasing the loop count will minimize this issue but not eliminate it. Give them weird defaults and initialize to custom local axes to minimize the issue. As a general rule, whenever you use an IK bone, place it directly after the bones it modifies, and increment the deform tier of all bones that follow. (No, you don't always have to do that, but doing it will prevent you from running into problems if you try to implement fancy stuff.)
4) Locked track. Often used in conjunction with damped track. Use a single bone IK chain, constrained to a single axis of motion with angle limits. Often requires initialization of local axes as in 1) above.
5) Copy rotation. Append. Axis limited copy rotation is to be avoided, even in Blender, but if you insist, you can use an IK bone with axis/angle limits, possibly tracking an append bone's tail, and append from that instead.
6) Limit rotation. Use an angle-limited IK bone to damped track the bone's tail. Like copy rotation, angle limits are to be avoided even in Blender (occasional cases where they're okay, but you can get interpolation problems easily because of how Euler angles work.)
7) Limit distance. Surface is easy-- use a single bone IK chain to acquire the position, then damped track and/or locked track appropriately to restore angle. Inside is easy, use a 2-bone IK chain. Outside, use a 2-bone chain, with the first bone longer than the second-- the difference in lengths becomes the minimum distance. To reduce this being a problem for weird situations, make this chain very very long (like 10000 units.)
8) Floor. Use a very long 2 bone IK chain, angle limited to remain planar (like for the typical floor case, rotation in MMD's global Y axis only.) As with an outside limit distance, not possible for every conceivable use case, but if you make your bones 10000 units long, it's not going to be a problem. To allow it to leave the plane but not cross the plane, allow X or Z rotation (one only, depending on orientation) in positive or negative (one only, determines side of plane they're constrained to) on the second bone in the chain.
9) Copy position/don't inherit rotation. Track with a long 2-bone IK chain, each bone equal lengths. Make a third bone with a -1 rotation append from the 2nd IK bone, parented to the 2nd IK bone. IK chain can be angle/axis limited to acquire X,Y,Z position only.
10) World space vs local space. Basically determined by parenting your IK bones to another bone (local space) vs locating them at the origin and parenting them to the world (bone -1, world space.) There isn't much I've ever wanted done in world space-- had some MMD floors in world space, I guess.
11) Anything having to do with splines cannot be done in MMD.
12) Anything having to do with bone scaling cannot be done in MMD. Although you can move a bone to a position exactly in the middle of two other bones (2 bone IK chain to target, then a 2 bone chain, half as long, appending rotation from that IK chain) to kind of fake stretch. I guess, conceivably, every vertex could get its own bone, then it would be doable. Well, except there's some bone limit that you might hit.
13) Action. Basically can't be done. People would like to have shapekeys driven by bones, which is at the far reaches of possible, because any shapekey is just a 3 axis translation, and you could potentially parent every vertex to a different bone, then use various appends to drive those bones. I guess, once again, there's MMD's bone count that would limit what could be done.
14) A note about movement appends. There's basically no way to drive translation as opposed to rotation about a center, but both cause position changes. Movement appends can be useful for controls, but any tricks like this rely either on rotation appends or IK chains to acquire position-- sometimes both, as when you acquire position via IK chain, then append from that chain to apply that position to a different bone's space. It doesn't really matter, just worth noting that you don't use movement appends to do any of this, and you don't need to.
This stuff could all be automated, although I pity the coder that would try.