My philosophy on this is "don't be afraid." It's all 1s and 0s to the machine when you're digital, so it's OK to dump 10 paragraphs into certain text boxes. If you want to do something, you can usually do it! A lot of programs let you paste images in directly nowadays.
If you're OK with having links to chats instead of the chat text itself, you can click the timestamps in a Slack chat to get a permalink . Sometimes I just copy the entire chat and paste it into Trello.
Which leads to "where". Most things I end up with are small tasks like bugfixes. Actionable tasks for the immediate. As much of that goes into Trello as possible. I'm not afraid of making multi-paragraph cards that copy the chat verbatim either (it's all 1s and 0s, right).
I also do the whole "screenshot" thing too. Take a screenshot and also paste it right into Trello.
Some stuff is important in the immediate but I'll throw away later. Temporary notes for things like user support. I use OS X's Notes app, which is basically notepad with tabs (I would likely use Notepad++ on Windows to accomplish this). It's all temporary notes, but still nice because it doesn't scroll up as other people start talking.
If I have something like a long-term reference, I try really hard to find a good place for it on a case-by-case basis. Usually that involves writing a text file (markdown) and putting it into Dropbox. On OS X I use LightPaper (a great little app), on Android I use Draft[1] (iOS has a thing called Drafts). Both apps are set up to point to the same folder, so I have these references on my phone too.
I also use text files for journaling what I'm trying to accomplish. For example, at work I'm working with a system that will physically mail documents back to me, so I wrote down exactly my operations so that when the docs get back to me I know what I did:
Sent two pdfs (located in Documents) on invoice `weFFEA123231`. One is Letter size instead of A4, another is A3 size.
Also sending Invoice `weFFEA123232` with just the letter-size page(`2015.pdf`).
A "user space unit" in PDF is 1/72nd of an inch.
Sometimes this log dead-ends, most recent entry:
For compressor and source maps, thing that's likely needed is to rewrite the JS compressor.
An easy solution would be
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I also use my calendar! I'll also just paste random stuff into my calendar for information I'll need at a certain event (for example reservation confirmation numbers).
This veered slightly off topic but tl;dr is:
Trello for tasks, Notes for temp notes, LightPaper for reference+journaling, Calendar for time-sensitive information.
[1]: http://www.mvilla.it/draft/