Just to clarify or make sure I'm playing this right, if my opponent has a figures adjacent to a door and I can shoot the door, can I use my surge to blast through the closed door and hit my opponent's figures?

Let's say on Reprogrammed on Training Ground

The two spaces on both sides of the door that share an edge with the door are adjacent to the door, but door blocks adjacency, so the two sides of the door are not adjacent to each other.

You can blast the other side of the door only if the attack destroys the door.

Also remember to check the current door rules from the FAQ.

See the lengthy discussion about doors around here. (I'm trying to locate it..)

This https://community.fantasyflightgames.com/topic/205507-blast-and-doors-question/

Takes you to this https://community.fantasyflightgames.com/topic/201851-blast-targeting-doors/ .

Read it, it has everything you will ever need to know about doors.

(Except that agains the rules as written you can target a door using a space adjacent to the door that you yourself occupy even if by the rules the door only occupies the adjacent spaces that are empty. Anything else would be silly.)