A bloke with a beer word in his alternate name would certainly know what he's talking about, BBaron. Yer right, our Septic friends are guilty of misusing "alternate" when they should say "alternative". "alternate" is a choice of one of two, "alternating current" is either positive or negative while an "alternate director" is a person who sits in place of the permanent director. "alternative" is a choice of one of many, you and I would choose an "alternative" beer rather than put up with Carlton Draught/VB/XXXX/Tooheys New fer instance.
"compliment" incorrectly used where "complement" is the right word is grossly abused on this site. And elsewhere. As a general rule "compliment" is a noun and "complement" is a verb. "compliment" is a nice thing to say, or do, "with compliments" usually means a small gift from a business or whatever. "complement" is used when two or more things go together, a nice fit so to speak. A nut "complements" a bolt, a THP "complements" a LHP. I think I'll stop there and leave it up to Dismal to educate us on some other complementary examples.