Some of the university libraries in Berlin are quite strict about what you're allowed to bring in (ie, no bags of any size). Fortunately, the Amerika-Gedenk-Bibliothek is close by and if they have such policies, they certainly don't enforce them.

Haven't been to the Grimm yet, but I remember passing by on the S-Bahn maybe a year ago and being excited about the huge new library under construction...I'm not in Mitte very often.