Are Label Errors Made By PCGS Worth Anything?

That stinks. I think it would actually help if you contacted them. I don't think a collector would want mistake, unless maybe there are exceptions

No, there is no special premium for what the TPGs call "Mechanical Errors" - typos on the labels, switched labels, etc. Contact customer service and they will fix it free of charge (sometimes if you ask nicely they'll even credit your account for your shipping charge).

Now sellers on ebay often put them up for sale asking moon money. Rarely do they sell for it.

Some of us collect slabs as part of the history of numismatics and we may want an error for the fun of it. I have one, in fact that I cherry picked from a Dealer at a show - it was an 1851O 3 Cent Silver in VF-30, marked as an 1851 (Philly). So it was worth maybe $10 more as the 51O than I paid as a 51. The fun part was that the discussion with the dealer (who is now a friend) was all about the loon across the way who had an 1952 Franklin ($200) marked as a 1951 ($350) who wanted something like a thousand dollars for the "MAJOR PCGS ERROR".

Look, if you grade 30m items, and make errors 1 time in every 10,000 ... there are a lot of mechanical errors out there...

If ya had at least 2 proof 40% submissions weigh both when ya get em back. If you have a large selection of ike's you may have grabbed a Clad proof by accident when putting your submission together.