Are the 4th edition expansions compatible with the 3rd edition core game?
Using 4th edition expansions with 3rd edition core game
Nope. All editions have different card sizes and backs, so cards from different editions can't be mixed. The main board of the third and fourth edition are different, especially the Inner Region, so cards will make reference to spaces that do not exist.
I would suggest reading my responses using 4th edition expansions in 2nd edition, most importantly the Dragon expansion. Tho I have almost no knowledge of 3rd edition, but I am fairly certain my logic on the matter would work. See here:
http://community.fantasyflightgames.com/index.php?/topic/95803-talisman-editions-conversions/
As said before the cards look different, so the small expansions are hard to mix as they add to the adventure and spell decks.
On the other hand, you should be able to use most of the big expansions, as they mostly use their own deck. (I never tried it, but I have used the 3rd edition forest in 4th edition. That worked fine.)
...but the 3rd edition board is much smaller than the 4th edition, so more than one of these will not be easy to fit around the board.
I will advice to switch to 4th edition
Well here is a comparison of the corners from 4th edition and 3rd edition along with how the 4th edition corners would not line up very well with the 3rd edition board. I suppose you could use them but you would have to institute a lot of additional rules and would lose the use of the cards from each edition going into the main adventure deck. Also, spells would be really hard to implement.
As you can see the new corner boards are almost as bis as the core 3rd edition board :-)
And that dragon tower is oh, so cool!!! :-)
The size is an issue, so you couldn' t use more than two at the same time if you wantet them next to the board. The adventure card and spellcards could't be used, but I can't see why you have to make alot of new rules. Fate is an issue, but I cannot see other obvious reasons why they would't work together.
When using the 3rd edition forest for 4th edition I made an "dryad" adventure card, even if the expansion works whitout it. Other than that I have not encountered any conflicting rules.