Action: When this unit enters play, all Undead units gain 1 power unit the end of the turn.

The way this is worded makes me think this could effect units which are not yet in play this turn. I'm thinking using a Raise Dead to put a Z-Dragon in from the discard at the beginning of my turn, pumping up my undead units in my Kingdom to get more monies then putting a bunch of now pumped up undead in the battlefield for a nasty attack. Have I wrapped my head around this Action correctly?

Also, it appears to be worded in such a way that this Action would buff my opponent(s) Undead units as well, right?

You are right. All undead units that are in play (also these of your opponent) when you play ZD, from your hand or from discard pile via Raise Dead, gains 1 power until the end of the turn.

Cool. I wanted to make sure that I get it before i try some new stuff this. Thanks for your hel…. wait, just to make sure, what about the units that are not yet in play but come out the same turn as the ZD but AFTER he hits the table?

The trigger of the Action of the ZD is: "when this units enters in play…" so, only the units that are in play when it comes in to play are affect of the effect, the units that enter in play after him no.

Bummer…now I'm not so sure this fella is going to make it into my first undead deck.

In the FAQ though on page 11

"Once a card enters play at the end of an
action chain, it is eligable to trigger any
of its own abilites, including those that
trigger off of it entering play."

Since the Zombie Dragon has to be fully in play to trigger its own ability it would be able to gain its own "P" from its effect. I don't think that it can trigger its ability untill it is considered in play.

"When a card is played, it is
considered to be neither out of play
nor in play. Playing a card triggers
an action chain, and the only way to
affect the card during this action chain
is with a “just played” effect. Once the
rest of the action chain is completed,
the card will either resolve its effect (if
it is a tactic) or enter play (if it is a unit
or support card)."

Yes Barakudas, the ZD gains himself the "P" from his effect when it enters in to play, not when he is played; also all the undead units that are in play, not the units that are played after him.