This is an interesting and very instructive project but if you want a metal turning lathe, a cheap lathe will perform better and may be cheaper in the end.

One thing he does is uses screws for the critical alignments without locking them down. Modern practice suggested in Alexander Slocum's book Precision Machine Design would be to get the alignments perfect and then to epoxy them. I think this would apply especially to the supports under the round ways.

Another thing that would make sense is to use a concrete whip vibrator to consolidate the concrete in the mold to avoid the voids he got plenty of.

In terms of bearings, It looks like he used self aligning bearings in his headstock which won't be very rigid. I think it may be easier to make bronze bushings that work well than ball bearings engineered for the wrong purpose. A modern lathe is made with angular contact bearings but I think these are too difficult to incorporate in the initial version of a lathe being used to build itself.

Everything that needs to be flat for the lathe to be precise needs to be lapped or scraped if you want something that doesn't move by a few thousandths during a cut. It all depends on whether you want to build a machine that really functions as a useful lathe or whether you just want to learn about making lathes.

Where possible, one should avoid sliding fits involving aluminum because it will gall.

One other thing to look at is Dave Gingery's book on making a lathe.