Cool! Glad you're enjoying it.
To be clear: there is a "Character Add-On" deck for each set. This deck is tied to the set, and really only makes sense with that set. (In fact, you pretty much have to have it to play with 5 or 6 players, because it has the henchmen you need for that number.) Also, it has characters designed for that set. I recommend always getting the Character Add-On deck for the set you are playing, but I would never use the Character Add-On deck from one set with another set.
That said: you can play characters from one set in another set. No problem there. Sometimes they will have powers that are now useless (say, a bonus against ships, when not playing Skull & Shackles), or they may be short on boons they need (but that can be remedied, see Class Decks).
A caveat about the Character Add-On deck and Wrath: you might not want to add the cards if you are playing less than 5 characters. That's because:
Different from Character Add-On decks are Class Decks. There are a slew of class decks. They have two uses: one is for Organized Play, and the other is to add boons when playing a regular set. (Also, the provide more characters, but really, you can download the character sheets for free and play the characters without buying the decks.)
You can add Class Deck cards to any set, so you could use them with both Wrath and MM.
The rules for adding cards are in the rulebook. In a nutshell:
-- When you are ready to play the first scenario of an adventure, at that time you add all the cards from that adventure to the box, mixing them with what you already have.
-- Similarly, you could add Class Deck cards with that adventure number at this time.
-- You do not remove any cards at that time.
-- Starting in Adventure 3, when you banish a bane with the Basic trait, remove it from the game (it will never be in a location deck again). You have the option of doing the same with boons (generally a good idea, except maybe for healing cards). Starting in Adventure 5, do the same for cards with the Elite trait. The rules for this are hidden on the Adventure Path card in the base set.
(Note: the character add-on cards are set C, which act just like B -- you can add those right away.)
Only add cards of a new adventure deck number when you begin playing that adventure. If you're playing Adventure B, the only cards in the box should have adventure deck numbers B or C (C comes from the character add on deck). When you start adventure 1, mix in all the 1 cards at that time, as well as any P cards you may have and wish to use (P stands for promo cards, the set doesn't come with any but you may have picked some up elsewhere; the adventure deck number of a P card is 0, even though you don't add them until you start adventure 1). When you start adventure 2, mix in all of the 2s, and so on. Never remove cards from the box when mixing new ones in, the Adventure Path card co rains the rules for when you start removing cards (elcoderdude's reply above includes the rule on the AP card). If you are using class decks, mix cards from the class deck in with the rest of the cards when you begin a new adventure (class deck B cards go in immediately, class deck 1 cards go in when you start adventure 1, cd 2 when you start adventure 2, and so on).
The reason for this is that mixing cards in early will significantly throw off game balance. Mixing in the character add on deck when playing with less than 5 players also makes the game harder. There are some official houserules you can use to reduce the difficulty of the B adventure and lessen the sting of adding on the character add on deck. Once you mix in the 1 cards, having two copies of Demonic Horde and Arboreal Blight is less painful because there are a bunch of other barriers added in as part of AD1.
Give that entire page I linked to a quick perusal as well, the page contains official errata on a number of cards and rules to clarify a number of things and fix some broken things.
For cross-set stuff, class decks are set agnostic but character add on decks are tied to the set printed on them. When you start a new set, you start over with new characters. You don't port over the characters that completed a previous set with all of their feats checked off, that would make the new set way too easy. You could re-use the same characters if you really wanted, but with over 130 characters to choose from you should try someone new :)
The class decks provide options that should work with every base set. Honestly, most characters from the sets work with every base set, though perhaps not _optimally_. There are a small number of characters where the lack of certain kinds of cards (ex: alchemical, firearms, corrupted cards, ships) deal a serious blow to the playability of a character.
Given that you currently only own Wrath, you can probably safely not worry about that for quite some time, though.