On the Research page, I would like to see a button for "Last Item Researched", which would open up the research tree to the last item used.

The button should go just to the right of the display for:
Production: nnnn research / hour [ More In: 00:00 ]

That way, to dump your research, you could click on the Research tab, then click on the "Last Item Researched" button, and immediately dump your research. It would save having to click lots of times to open up the research branch you needed. And it would remember where you were.

Are you aware that clicking the arrow jumps through a lot of the research with each click?

Probably easier coding to tell that arrow to jump to the end of your research tier.

Eh, either would work. +1 to both in the hopes that one is implemented.

+1. I hate having to click the arrow button so many times to get to the last block

Keep the left/right arrows as they are now. Add left/right double arrows that take you to the beginning/end of the list.
So you'd have: [<<] [<] [Research List] [>] [>>]

Or maybe have the columns right-justified rather than left-justified. Like we've (especially ODragon) been asking for for nearly 3 years now...