When something is alternate, it tends to switch between two states, rather than when it is alternative, which means what most people intend alternate to mean.
In other words, saying someone lives an alternate lifestyle implies they have a lifestyle every other day.
In recent years, however, this mistake has become so common that even the Oxford English Dictionary has started to merge the two meanings, giving each meaning as "alternate" to the other

She would have me write a paper Then she would correct one mistake at a time, while having me redo the paper each time. It took hours and hours. As tough as it was, it worked and I'm happy for it. Now I see errors all the time; I can't look at my local newspaper without thinking that they really need a proofreader.
Unfortunately, this sort of practice has completely vanished from at least the Australian Queensland education system. I'm rather glad, then, that I have English as a second language, and understand it thoroughly only because I learnt German (so violations of the subjunctive still hurt me deeply

) the hard way, at school.
Excuse my (second) rant