PvP gear is designed to dish out and protect against burst DPS. It does very little against sustained damage. You might not have noticed it, but I bet your groups have.
Only use PvP gear as a "filler" for PvE purpuses, and replace it as soon as possible.
It depends. If you have a PVE piece that really is a better DPS choice, wear that. Hit is not very important against normal or heroic bosses (level 71 and 72 I believe). Raid bosses (Level 73) are where you need large amounts of +hit or +spell hit, but I wear my PVP gear through dungeons and heroics all the time. Weapons, helm enchants, and the tiny amounts of hit on PVP gear should cover that.
Honestly for DPS, Gladiator gear may be better then almost every dungeon blue. If you have KZ epics or better, they are probably the best DPS choice though, but it depends.
For example, rogues can look at the charts on www.shadow-panther.net. Go to the PVE Max DPS table, and as a ROGUE, you could compare different pieces of armor. It's too bad I haven't found other class websites like this, because on my rogue I use it alot.
For example, rogue helms. If you're using the S1 helm, there are actually 2 better blue items for max DPS (Helm of the Claw- SV quest reward, and Wastewalker Helm- the 'Heroic' D3 set, from heroic Durn). But, if you have the S2 helm, that is better then any dungeon blue. If you have the S3 helm, that is better then anything out of kara, gruuls, and is only marginally behind the T5 helm in terms of PVE Max DPS. It also beats the T1 engineering goggles in PVE. Note the S1 helm is still better then the normal D3 helm, the 'Assasination' set. So my point is, PVP gear is not always bad for PVE DPS. You should go on a slot-by-slot basis, and compare the actual stats. Don't just jump too conclusions on items, saying "oh this is crap because its PVP, or this is great because it's from kara".
Anyways, for tanks and healers, often quality dungeon and heroic blues will be better for healing then gladiator gear.