How would anyone know that he was bringing a bunch of ammo into his apartment? Ammo is shipped in cardboard boxes like any other parcel, and only the blue and white “ORM-D” sticker is likely to give anything away.
And even if anybody knew he was buying bulk ammo...it’s not illegal (in fact it’s a way to save money in the long run), and for all anybody knew he just went shooting on the weekends like most bulk buyers do. (Even if you’re just shooting a bolt action, 100 rounds can go by kinda fast....)
Think whatever you will, but since Holmes was unknown to all his neighbors, if they had known about a few of the items he was acquiring, some would have wondered what he was up to. How suspicious they might have become would have depended upon how much they might have learned. There was a great deal to learn about Holmes and all his recent acquisitions.
People can engage in all sorts of legal behavior, the sum of which might justifiably raise suspicion, or draw the attention of law enforcement. We have the same possibility when people are acquiring ingredients needed to make crystal meth, or to make moonshine.