The tailift is a biggie if you want it kept all original. Any heavy gauge strings will make that worse. Other things to check are the frets, they were notoriously soft and roundwound strings would just eat them up. Also, check the fretboard and binding near the body. Occasionally this would separate or the truss rod would poke through on the older 4001s. The 4003 had a much more substantial neck to address this issue. Then you have the dreaded double truss rod which can be a real pain for those not experienced in using them. Special wrenches are needed for them too due to the lack of space in the headstock. There's also that unbelievable crap bridge system which belongs in the stone age imo. The strings need to be loosened to intonate them and it's trial and error for the best part. The strap pins are another thing. Rickenbacker in their wisdom decided to use pins with a thread designed for metal and not wood. The result is that they would occasionally come loose and would need to have all manner of bodges to fix them, although the previous owner appears to have replaced them with straplock pins on this one.
I get that it's a lovely colour but imo the latest Rics are a whole lot better. All these issues that plagued the early 4001s have now been addressed with a much better bridge, more tonal options and better hardware all round. I love mine and it cost less than the one you have your eye on too.