No, because dimension door does not allow you to take any actions until your next turn, this includes attacks of opportunity. If the caster of dimension door was adjacent to another ally and transported that ally along with them then the caster wouldn't be able to do anything, but the transported ally could. That includes making atatcks of opportunity when they are provoked, such as when casting a spell.
But, and this is a big but depending on how you rule on readying actions, I would also allow the spell caster to take a 5ft step before actually casting. Many people disagree with me on that, and I don't personally care for the way readying actions can impact turns.
There is that, but an attack of opportunity does not take an action. It's neither standard, full-round, free swift or immediate. That's why I wasn't sure if it applied here.
Dimension Door is a very old spell that hasn't been updated since it first appeared. At the time it is my understanding that AoO either didn't exist or weren't non-actions or some such. Either way, the specific line of the spell that says no action is meant to be quite literally as in absolutley no action that isn't merely reflexive in nature (breathing, avoiding an attack, etc).
Edit: There is another thread here which disagrees with me. Now, I'm not so sure.
The argument does hinge on the AoO are not an action, but I really don't like that, and I feel the intent of the original version of the spell really meant the caster couldn't do anything actively, but I'm not so sure now.
I think the Rules as Intended per the spell is no, you can't even take AoO.
I think the Rules as Written specify that you can't take any action and attacks of opportunity are listed as not an action.
I definitely lean toward my interpretation of RAI in this case. I don't think there has been an official developer comment on the issue.
I'd allow it if the character took the Dimensional Agility feat as this allows them to finish up the actions on their turn.
I'd allow it if the character took the Dimensional Agility feat as this allows them to finish up the actions on their turn.
I agree 100% on that because it allows you to take your remaining actions.
I think that it's going to be up to the GM. An AoO isn't an action - but in order to take an AoO you must threaten, and to do so you must have the capacity to make a melee attack into the square when the provoking action occurs; since Dimension Door specifically states you can take no further actions until your next turn, you technically don't have the ability to make a melee attack.