I built off the same plans. The best advice I can offer as far as registration goes, is to make sure that each of the 2x4's used for the arms is the exact same width. The plans state that uniform length is important, but my opinion is that the width is more important than the length. When you set the width of those guide pieces on the side, if any of the arms is narrower than the one you used to set that width, it will allow the arm to have side to side play. Also check the hinges that connect the arm to the turntable and make sure there's no slop. You can check it by bringing each arm down into the position it would be when you were printing, and try to move the arm side to side (I numbered mine to make that easy keep track of which ones I was inspecting). If you're registering a screen, if the length of the arms is off by a fraction of an inch, it's not going to be as noticeable than if the width is too narrow, because that's what is going to throw your registration off. Especially if you're using that arm to do white over a dark color shirt, and do 1 stroke of ink, flash, then another stroke...it's most likely going to have fuzzy edges on the print. Length you have more leeway to adjust in moving the screen under the clamps, but width, there's not much to do besides try putting shims on the side of the arm or just replace it altogether.
Lots of people laugh at this design, but it's a lot more sturdy and stable than it looks if you use both screws and wood glue in all the joints, and a good quality bearing for the turntable. It's not going to rival a $1000 commercial press, but it's not meant to. You just have to have realistic expectations of it; it's just a very basic 4 color press, no micro registration, etc. I agree if you are planning on doing large quantities, it would probably be best to get a commercial press, but you have to start somewhere. I was in the same position where I wanted to get into screen printing and didn't have the funds for a commercial press.
The best way to learn anything is hands on, and this is a way to start learning the fundamentals of printing. Squeegee angle, pressure, etc, and finding what techniques work best for you. You can read all the books and websites about screen printing, but the best way to learn in my mind is to start putting ink through screens. If a home built press is your only option to do that, then do it. If you outgrow it in time and need to upgrade, by then you'll have more knowledge and technique under your belt to select a commercial press, and probably the funds to do so. Because I can tell by reading your posts that you have a lot of ambition and motivation to be successful at it.
Good luck with it.