I have a 1975 Vette and I'd like to update the old 3-speed tranny. What are the problems with installing a 700R4 over drive unit in this car. Thanks.

Not too bad, really. The '75 has a 400 trans in it now. The good thing is, the crossmember you have will work fine, but you may have to elongate the two mount hole for the mount to bolt up.
Then you'll also need all of the normal 700-swap items, such as the TV cable , bracket, and carb linkage adapter, as well as the dip-stick/tube. You will need to have some driveshaft work done, also, which, in your case, will also include changing the front yoke.
There are DIY kits to modify your shifter, too, so that will work.

You can search "700R4" right here on this site. There's a lot of good info. on this subject.

I'm having one put in to my '79 right now. I'm not that good with a wrench, so I'm paying to have it done. However, the threads here gave me a good idea of what parts were involved.

I say "go for it!"  Keep us posted.

Kevin

I am about to turn the key on my 700r4 swap this weekend!! Will post my updates and results for all. A great website to review is Bowtie Overdrives. They have a great 3 part series on 700R4 TV cable set up, which is one of the most critical success factors for the swap.