In general, imperfect action is better than inaction. From a brief glance at the table of contents in the first edition, it looks like they're fairly similar- the second edition has an extra chapter (of which a few sections are great and several are skippable). Many of the sections have extensions from work done after 2000, but the basic concepts underwent little change. I would imagine that the second edition has fewer errors, but without a detailed reading I can't tell how significant that is.

The main trouble you could get into with reading just the first edition that I can think of is a few of the definitions which underwent significant revision to exclude some corner cases where they misbehaved.

I think I would ask the library if they can order the second edition while starting to read the first edition.