Lots of our trees locally are slow to leaf out.  Most of our elm trees are being slow, especially upper leaves.  We had a freeze event in mid-April that I think is the culprit.

I would not worry too much about it at this point.

Kurt

The branches that have not leafed out are dead. The roughness of the bark on the dead branches are the only difference I can see between the live branches and the dead ones.

I've attached some more recent pictures.

Your new pictures got it!  It is European Elm Scale, an insect that feeds on elm trees, and has been increasing in later years on Siberian elms.  Prune the dead branches out of the tree.  If you see these scale bumps on green twigs, you can scrape them off using a pot scrubber sponge successfully.  Insecticides are only effective early in their development (crawler stage), but after they have hardened off, insecticides are much less effective.

Normally these insects will only kill branches/twigs and not the whole tree.

I hope this is helpful!

Kurt