It should stitch perfectly at full stitch length. I have had a similar issue with reverse stitch a few times, but I managed to sort it out. It might not be very difficult, but it can be lots of work to clean up an old 201. I have fixed up two and the bobbin / hook / race / feed area needed lots of attention; cotton swabs, tooth picks, etc., scraping out muck from corners and polishing metal parts. Grime behind the needle clamp can cause problems too.
With the 201 make sure the bobbin is in the correct way; the thread is properly in the tensioin spring; the needle inserts with the flat side to the left and threads from right to left. Match thread weight and needle size well. You have probably been through it all with your model 15. The bobbin case on the 201 is a bit tricky to take out and clean, but the illustrations in the manual is very good. The tension is a bit more fuzzy than on a 15 and needs to be just so for certain types of work like free motion. It's all about getting to know it's finer points and like other's have mention it's not difficult.
This one is good quality on my screen. There are a few
service manuals available too