These error messages could indicate that the AAC files in question are corrupt, or they could be bugs in FFmpeg. There are different profiles that comprise AAC and AAC-LC (low complexity) is just one profile (and the most basic one to implement). But different profiles implement different features. If an AAC stream claims to be AAC-LC and then contains the long term prediction (LTP) feature, then that's an invalid bitstream.
Same goes for the other errors you encountered. FFmpeg is parsing the stream and finding different pieces which exceed certain thresholds defined by the specification.
It's possible that FFmpeg is doing the wrong thing-- are any other programs (not based on FFmpeg) able to deal with these files correctly? Also, be sure that you have the latest, up to date FFmpeg version.
If you're interested in the specific AAC features that FFmpeg supports, they're listed in the comments at the top of libavcodec/aacdec.c.