I always tell my students at all levels that there is no excuse for not spell checking one's writings. There are rather good spell-checking programs out there, and one should use them to spot obvious typos.
Spell-checking programs, however, are no substitute for careful proof reading of one's papers. I was reminded of this fact of professional life some time ago when, while reading the revision of a journal submission of mine, I spotted the mention of a "format for impotence of operators" (in lieu of "format for idempotence of operators"). It would have been embarrassing, but admittedly amusing, to send the paper off with that typo left unspotted, just as it was entertaining for my students to attend a lecture mentioning a "poof technique" (rather than "proof technique") on a slide :-)
No spell-checker can find those typos. I'll use them to motivate my students to proof read their texts with care.