There may be a plugin which could assist. Dunno if John Beardy's Metadata Search & Replace plugin will do it(?)
Another option is to load xmp into a text editor (or xml editor) which has spell-checker, modify it there, then re-read in Lightroom. This works better for xml sidecars than embedded xmp, but you can extract the xmp for any file type into a sidecar using xEmP, and then re-read after making the spelling corrections.
I was offering an option for the mean time, which may serve as fodder for brain-storming, even if not acceptable as is...
I understand that your request is for native support in Lightroom, Adobe understands this too (despite lack of direct response...).
Got a "super-grep" util with spell-checking? - you could do the whole catalog in one swipe - using xmp. How about a TextPipe Pro? - that'll do it too - directly to database (disclaimer: dunno if they support sqlite databases). Did you check John Beardy's plugin? - I know he was entertaining spell-checking, I just don't know if it ever got done.
Do you know of a utility that will do spell-checking via command-line in Windows (I don't think it's built into OS). And what command might accomplish it on Mac. - part of the problem is cross-platform support. Apps that only target one platform can integrate platform-specific things more easily... It could be a no-brainer on Mac, but require royalties for a proper Windows solution...
I could easily write a plugin to do metadata spell-checking once I had the gut spell-checking pieces in place and operational, but:
A. I don't
B. A lot of times people wouldn't use it anyway, being a plugin that implements a non-essential function, when what they want is native support.
Thanks. I see where you are coming from. I'm getting pressure from collegues to incorporate Photo Mechanic in my workflow. Something I'd rather not do. Lightroom is so close to meeting most of my needs. Spell check and xmp support of vidio files (listed seperately) are two areas that stick out for me at this time.
Regarding spell-checking, it seems there are two somewhat different albeit related problems:
1. How to fix-up spelling mistakes in metadata past.
2. How to assure no spelling mistakes in metadata present/future.
Regarding #2, third party spell-checkers seem almost as good as a native Lightroom implementation would be - in some ways: better.
For example, on Windows: MicroSpell is a super spell-checker: in default installation mode you have to remember to hit a hotkey (Ctrl-F12) to check current field (there is also as-you-type mode, but it makes me nervous, and I didn't try it), but it is quite a nice setup - the UI can be a bit daunting at first, but then it seems straight-forward and quick, after you get used to it.
Regarding #1, MetadataTransformer will allow you to spell-check & correct all of your existing metadata. It's default configuration for Windows is useful out-of-the-box for spell-checking captions and/or headlines (provided you download & install MicroSpell in default location), whereas Mac users will have to figure out how to wire it up (if they let me know how to do it, I can incorporate in next release). If you do give it a whorl, please contact me directly for technical support, rather than subsuming the Lr forum for it - thanks.