waynefromvirginia beach's response made me realize what's going on.
I've been having the same problem, and now, with some experimenting, I think I know why.
Under Lion, when you replied to a message, Mail sent it from the email address that matched the To field of the original message.
Under Mountain Lion, when you reply to a message, Mail sends it from the email address of the account whose inbox the message is currently residing in (unless you've changed the settings to always send from a certain account).
In many circumstances, this is the same thing, so many users wouldn't notice a difference. But in some circumstances and for some users, this makes a huge difference and causes undesirable behavior.
For instance...
Let's say I have two email accounts: bob-work@example1.com and bob-home@example2.net. I have Mail set up with two accounts, "Work" and "Home," each checking mail from (and replying from) its respective address.
Under Lion, any messages I receive that are addressed to bob-work@example1.com will be replied to from that address, and messages that are addressed to bob-home@example2.net will be replied to from that address. Simple.
Under Mountain Lion, though, things are different. Any messages in the "Work" inbox will be replied to by bob-work@example1.comregardless of what email they were addressed to, and any messages in the "Home" inbox will be replied to by bob-home@example2.netregardless of what email they were adddressed to.
As long as each of those account inboxes is only checking its respective emails, and as long as I only reply to messages while they're in my inbox, everything works the same as in Lion.
But here's where it creates problems.
If one of my email addresses is actually an alias that forwards to another address (like if I have multiple work addresses that forward to the same account, or if I use a .Me address or other service to gather my email in the cloud before I download it), then those emails won't be in the expected inbox and therefore won't be replied to by the correct email address.
If bob-work@example.com forwards messages automatically to bob-home@example2.net, then those messages will be in my Home inbox and will be replied to by my personal email address under Mountain Lion instead of my work email address as they were under Lion. Mountain Lion doesn't seem to care who they were addressed to; it only cares which inbox they're currently residing in. If I manually (or via rules) move the messages to the correct inbox, then I can reply as expected.
Similarly, if I reply to messages from a folder rather than from my inbox, Mail no longer knows which email address to use for replying, so it just uses the one associated with the first inbox in the list (I think).
I much preferred how Lion handled these situations, and would rather that it be at least an option to switch back. In the meantime, the best workaround I can think of for people who forward their mail from one account to another is to use Mail's rules to put the emails back in the desired inbox before you reply to them. This doesn't do anything for those folks who reply from non-inbox folders, though.
Let me know if this helps!