Applying for a journalism internship I really want and of course in the last line of the email I wrote "your welcome to call" instead of "you're welcome to call". Should I acknowledge this mistake or leave it and hope it doesn't matter? Of course the context of this industry makes me think it's more important.
You screwed up. Don't make is worse by pointing it out by misguidedly trying to "fix" it.
Think about what they know and what pointing out the mistake will tell them. Maybe they didn't notice. If they did notice, most likely they realize it's a small typo. Assuming the rest of the resume is well written, at worst that just says "sloppy". Do you really believe that they think you don't know the difference between "your" and "you're"?
You're guilty of letting a mistake slip thru, not of making one in the first place. Therefore, pointing out the mistake won't do anything useful. You still didn't catch it when you should have, and catching it after it's too late doesn't really mean anything. On the other hand, it makes you look like a weenie.
Fix the resume now. If you see them again, bring the updated copy and give it to them without any fanfare. If they ask what you changed, just say you fixed a typo and some minor wording (it would be good to fix something else too).
David K pointed out that this slip-up was just in a email, not on your resume as I was somehow assuming.
Seriously!? Forget about it!
While they may well expect that you carefully proofread your resume, or any written example copy you may have submitted to them, they're not going to hold you to the same standard for a one-time email. Whoever read your email message has most certainly made a few mistakes in emails of their own.
This is a non-issue. Trying to "fix" this will seriously make you look like a weenie.
If it was a typo on important information e.g. on contact info or names, a follow-up email with a correction would be appropriate. But for a common misspelling like this I would be more annoyed by a follow-up email on the typo than the typo itself.