Ok, wiseguy. You come up with a better explanation for why the Klingon bridge looks different.
I DON'T HAVE TO--that's the beauty of FICTIONAL entertainment. I just take what I see at face value, to start, and decide AFTER I've experienced it (film, music, play, etc.) if it was worth the time, money and effort to see. But if you must have an explanation--the people working on Star Trek IV probably thought the version in Trek III was too bland (and hey, it was the same director for both, to boot--a certain original icon of TOS, IIRC. Now what was his name....?) and did not capture the "Klingon feel" sufficiently for the far lengthier screen time it would receive in Trek IV (for the very short time it was on screen in Trek III, the original was serviceable). So Nimoy (yeah, that was his name--too bad he just pissed all over continuity like that

) and company, understanding (unlike some, apparently) that IT'S JUST ENTERTAINMENT decided to "spruce things up"--because he could. That's it. No "rationalizations" necessary. They made a movie and saw an opportunity to revise the visuals in an area that was, in their view, lacking in the previous effort. The same thing is at work today.
No, it isn't. If the filmmakers had wanted to be slavishly bound by continuity, they would have either paid whatever Alley demanded to reappear or they would have "killed her off-screen"/"last minute emergency takes her somewhere else so we don't see Saavik". But the writers thought the character was integral to the story, so they recast her. Just like Rachel Dawes being recast in The Dark Knight--Holmes was unavailable (pregnant during the shoot), so they just found someone else. If they wanted to be "slaves to continuity" (and only their own Nolanesque take on it, at that) they could have written her out of the story to avoid the issue.
It's all ENTERTAINMENT. It's not a religion or a life or death issue. Now, if, in over 700 hours of Trek, not one single iota of "continuity error" had EVER cropped up, then perhaps I'd be slightly sympathetic to the "purists". But I've been watching Star Trek in all of its versions (save the fan films) since 1973 and I've lost count of the "continuity errors" I've noticed (and I do notice them). I simply don't let visual cues or small details like middle initials or Khan remembering Chekov get in the way of enjoying Trek. Far less stressful that way.