A mistake here is always a matter of written grammar error, as all these sound the same when we speak.
Many things equals a lot of things—two words. There is no such word as alot. A and lot should always be written as two separate words.
(Then there’s allot. That means to assign or allocate or apportion something, or to give it as a share of something. For example, “Line up, and I will allot each of you your piece of cake.”
To repeat, don’t ever write alot. Ain’t no such word. : ). If you are referring to many things, it’s two words: a and lot.