(apologies for any injury caused by the apostrophe in the title)
I'm using FMPA 14.0.4 on OSX 10.10.5 and I'm editing a layout with a text field.
If I type "blerg blerg's " in the text field, both terms are underlined by the spelling checker. I can right click on "blerg" and select "Suggested Spellings > Learn" to add it to the dictionary. However, when I try to do this on "blerg's" it does not stop underlining it.
If I exit the layout and re-enter edit mode, it is highlighted again. If I right click the word and select "Suggested Spellings > Spelling...", and then try to click "Learn" on the spelling dialog, it indicates that it is a questionable word, but if I click "Check" the status changes to "Correct Spelling"; however this does not stop it from being underlined. If I click "Learn" in the "Spelling" dialog, it says "Word already in the Main or User Dictionary"
I think you may be using "Smart quotes", and it would seem that this messes up FileMaker's handling of apostrophes (since the apostrophe is treated as a single quotation mark).
Try turning smart quotes off in File options, type the words again, and test to see if it makes a difference (it does for me).
The crux of the biscuit is the apostrophe.