"If I understand the rules correctly, downvoting is used for not agreeing with a comment, and flags are used for inappropriate comments."In theory, no, downvoting is not supposed to be used to disagree. It's supposed to be used to move "stupid" comments (inarticulate, illogical, poorly argued, etc.) down towards the bottom of the screen. Flagging, on the other hand, is meant to call out wildly inappropriate, offensive, or completely off-topic comments.
A few hypotheticals:
1) I see a comment that is well articulated and generally inoffensive, but I disagree completely with its premise or its arguments --> I do nothing.
2) I see a comment that is irrational, illogical, poorly constructed, whiny, or off topic --> I downvote.
3) I see a comment that is extremely offensive, completely unrelated to the topic at hand, spammy/astroturfy, or clearly intended to instigate a flame war --> I flag.
That said, many people seem to use downvotes to disagree with a comment, and I'm concerned that lowering the downvote threshold will lead to even more of that behavior.
Maybe the problem is that downvoting and flagging share too close of a hypothetical use case. Downvoting is clearly easier to do, and it's doable in the main thread view. So that could be why people routinely use it to disagree with comments. I have flagged maybe a grand total of one comment in all my time on HN, and I generally regard flagging as an option of last resort. (It could also be that I arrive at various threads after the worst stuff has been flagged and removed, providing me an artificially sunny view of the threads).