I can think of two problems.
TMI is usally done be log levels so we can decide how much we want to see at a certain time error, debug, info, ....
the leaking of private data is more tricky because it's a question of definition also it depends on exposure. If i 'leak the data' to my harddisk and it's concious, secured, ... etc out of protocol reasoning based on my field of work it's not that bad.
if i console.log the secret hashes of my system in the browser ... that's a different topic.
These are my initial thoughts. I probably am missing something.
Sambhav choradia
Associate Software Developer
Agnius Vasiliauskas
php-dev
Question is marked as Javascript subject, however it could be interesting for other languages too. So I'll answer for generic case.
The biggest drawback of logging system over-usage is that it may deplete disk quota, thus crashing process / operating system / computer. So use it wisely - log only what you need and when you need. And from time to time - check computer for unnecessary or too old logs and purge them from the storage.