What I've always had trouble believing is that the Klingons would use cloaks. I mean, if Starfleet wouldn't "skulk around," why would the Klingons? Wouldn't they consider it dishonorable to sneak around and hide? Sure, you can somewhat rationalize it on the grounds that warriors value stealth, and that you have to decloak to fire so you're still facing your enemy openly. But the whole idea of Klingons using cloaks is basically an unfortunate artifact of Harve Bennett originally writing ST III with Romulan villains and then failing to change the technology when he changed the species.
Isn't that a bit back to front? The search for spock pre-dates TNG Klingons by about 3 years - while they are visually the same, I don't think the "honor" aspect of their culture was around then was it? Those were TOS klingons updated for the big screen... or maybe not - I haven't seen the search for spock in over ten years so could completely misreading how they were in that film....
Now that still leaves the question of where the cloak comes from - I just chalk that up to them stealing one and retro-engineering it into their ships, but there isn't anything wrong with them having a cloak as they are shown on the screen.