I am looking at two opportunities with the same employer, either one I would be very good at. Should I apply to both? Or should I pick only one? I worry that applying to both makes me look like I'm wallpapering the internet with my resume, whereas if I apply to just one, I worry about missing out on the other opportunity if my qualifications come up short.
Talk to their HR person. Ask them how, based on the size of the company, industry they are in and culture, whether it would make sense to do this.
Personally I would recommend you pick 1 and go for it because:
Imagine the conversations otherwise -
yeah, since you asked (e.g. found out), I also applied for position Y because, er, ...
I'm excited about this position. What about the other one? well I'm excited about that too...
Well, I didn't get position x with Bob, but now I'm applying for this one because, er...
As you can see, while there certainly may be clever answers to the above, the overall impression I'm trying to give is that this is just not a place you want to be in !
Apply for both. You never know which one will be the one they want to interview you for. They may have different hiring managers who also have no idea you are applying elsewhere in the organisation or if it is the same person, he may be happy to know you are interested in both because he may have lot of good candidates for one and nobody but you that is good for the other.
If it gets to interviewing though, let them know you have applied for both jobs. If both managers are interested, then they might interview you in the same session and they will have a chance to consult together to determine the best fit if both want to hire you. You wouldn't want to start a new job with a manager mad at you because the other guy stole you away from him and he didn't even know the other guy was looking at you.