The poem says it all - Spell check can catch some things, but not all, and substitutions can be a larger problem. At least a misspelled word is still the same word - Spell check can, in its wisdom, substitute a completely different word, which is worse. Spelling ability does not necessarily relate to intelligence or ability. The larger issue, as has been mentioned here, is the perception that people get when reading any kind of report. We associate poor spelling with ignorance.
If you have a spelling problem, it only makes sense that you use every possible tool you can to get it right - spell check, dictionary, your partner. Practice the terms and words you have trouble with. Keep a sheet of words and terms that are difficult for you with you at all times - refer to it if there is any doubt. Add to it as needed. This is faster and easier than packing a dictionary.
This works with grade-school kids. Should certainly work with adults.
Good luck!