So the Dimensional Shambler can Dimension Door at will, and has Dimension Mastery which states: A dimensional shambler can take actions normally after using dimension door effects. A dimensional shambler under the effects of a dimensional anchor or dimensional lock spell can ignore the effects of the spell for 1 round by making a DC 25 Knowledge (planes) check as a move action.
However, Dimension Door is a standard action, so if the shambler uses dimension door, does it only have a move action left that round? Or is it able to dimension door, then attack/move/etc?
A dimensional shambler can take actions normally after using dimension door effects.
Normally, after using Dimension Door, you can't take any other actions until your next turn.
Using his Spell-Like Ability is still a standard action unless otherwise specified.
And since normally, you cannot take actions until your next turn, you would be unable to make attacks of opportunity, because you're still "recovering" from the dimension door effect.
The Dimension Shambler is still ready to make AoOs, and can take move and swift and immediate actions.