While playing tonight I noticed that Totem of Gork says the +1 attack/defense bonus applies to "units in this zone." I played the card into my battlefield, so does that mean all units get the bonus, including my opponent's units in the battlefield, or just my units? We went with the strict interpretation and applied the bonus to units from both sides that were played to the battlefield, but I can't find any official errata or discussion regarding it.

"This zone" = your battlefield. If it affected units in all battlefields it would have said "corresponding zones" or something similar.

I don't think that's correct. The rulebook simply states "The Warhammer: Invasion LCG is played in three zones: the kingdom, the quest zone, and the battlefield." All other cards that only apply to your units/developments/etc. clearly say "your" in the text, but this doesn't say "your units" or "your zone" it just says "units" and "zone." This leads me to believe that if I play the card to the battlefield zone, all unit cards in the battlefield zone benefit from the bonus effect.

Just checking the Empire cards, your interpretation would mean:

"Limit one Hero per zone" would mean 3 Heroes total can be in play, not 3 per player.

Greatswords would gain P even when an opponent's Unit entered the zone they are in.

On the Dwarves, Ironbreakers of Ankhor would have Toughness X, where X is the number of developments you + your opponent have in that zone. Dwarven Cannon Crew or Dwarves Masons could play their special ability to the opponent's zone.

Regarding "Limit one hero per zone," what you said (regarding only three heroes instead of six) is precisely what the FAQ says:

“Limit one Hero per zone”
If a player has a copy of a Hero in
play, he cannot play, take control of,
move, or put into play (via a card
effect) another Hero into that zone.
His opponent also cannot play, give
control of, move, or put into play (via
a card effect) another Hero into that
zone.

That's the way we've been playing if you get a Hero into the battlefield before your opponent, for example, then your opponent can't play a hero into the battlefield. It seemed silly to us, but if you strictly interpret the game's definition of a zone that's really the only way to handle it.

I suppose I'm just reading this wrong, but I really wish they would better clarify what a zone is. The rules say there are only three zones, but the cards indicate otherwise.

No the cards don't, you have three zones. Your opponent has three zones. Something that will effect a specific zone of both players says so, something that is zone independent won't say zone at all. Something that affects only your opponents zone will say so.

Looking over a bunch of other cards, you guys are all right. There are three zones per side instead of three total. Many thanks to all of you for getting back to me so quickly with the clarifications.

No problem at all. Sometimes we read way more into a thing than is there. Other times we fixate on our first impression and it takes a full shift of perspective in order to see it another way.