It's self-contradictory. One sentence says they take their bonuses with them, but that appears to just be flavor text for the sentence after it, which says that you keep the bonuses on skill checks, attack rolls, and damage rolls wherever you go. The ability to dimension door is not a skill check, attack roll, or damage roll, so you wouldn't take it with you.
The problems with this interpretation:
1> The Fly speed on weightless planes is explicitly said to only apply there. None of the other specials say that.
2> Most of the other specials would be useless if they only applied on one plane, making the class far weaker than it should be, especially considering the class can't plane shift itself.
The ability to dimension door once every 1d4 rounds isn't too unbalanced, IMO, since 1d4 rounds can be a long time in most combats and you waste a round just recovering from the jump. And, you can't take it until 11th character level at the earliest. But it just doesn't make much SENSE to be able to do that on the prime, especially since dimdoor lets you take people with you.
(Solution: change it to dimension slide, the close-range self-only Psionic power, but on Shifting planes you get teleport instead. Likewise, the Weightless one could let you levitate on normal planes)
The abilities NEED to be good. This class is clearly intended for Rangers, since only they, Bards, and Wizards have Knowledge (geography) as a class skill and Rangers get Endurance for free at level 3. Yet, compared to a Ranger you have 2 fewer skill points and a bad Reflex save, not to mention the loss of Evasion, bonus Feats, and spells. The planar attack/damage bonuses make up for the lost Favored Enemy points and the skill boosts for terrains make up for the lower skill points, but the special abilities you can select need to cover the rest of the gap.
There are a few other problems I have with the class. Don't get me wrong, overall I love the class. I'm currently convincing the DM to let me retroactively alter one of my characters so that he can take it.
1> Why get Fire Resistance 20 if Fire planes do 3d10 damage per round? You'll still take damage pretty quickly if the DM rolls anything above average.
2> If you pick Aligned plane, it says that "spells and abilities that harm the opposite alignment don't affect you" and that "you have the dominant alignment of the plane with respect to magic."
The Prime is True Neutral, so while on the prime things like Detect Good fail because of the second one, and abilities like Smite Good fail because of the first one. So far so good. But does this mean that nonmagical abilities that don't harm you directly but are based on alignment would still work? (Example: a Ranger who picks "Good Outsider" as a favored enemy would still get his bonuses against a Hound Archon Horizon Walker on the Prime, except maybe the damage bonus)
Does this also mean that an Evil Horizon Walker can pick up a Sun Blade without negative levels? It's magic, after all, so it should be fooled...
3> If you pick Desert it says you can't be Fatigued, and then says that if you get Exhausted you become Fatigued instead, but didn't it just say you were immune to Fatigue? (I know what it MEANS, I'm just saying it's badly phrased.)
4> If you're giving planar bonuses, why isn't Knowledge (the planes) a class skill?
