I figured performer salaries were an issue and a reason why the budget was an issue in the third season. However, given only three of the cast members received top billing, I'm not sure how much of an issue this was in reality.
Shatner, Nimoy, and Kelley were not the only three actors with contracts that guaranteed annual raises. Koenig, Takei, and Doohan also received annual raises. Nichols was was paid as a day player, although she may have received a raise at some point. Since she didn't have a contract (only a hand-shake deal), there's no paper trail as far as I know. I don't have her memoir, so I can't consult it for more information, but it might say.
Inside Star Trek: The Real Story
Either way, I didn't get the impression that the last season was substantially cheaper looking than the others. The writing took a nosedive. I think "That Which Survives", or "This Way to Eden", "Spock's Brain", "And the Children Shall Lead" and "Turnabout Intruder" prove this. There were still a number of good, classic episodes regardless.
suggests that an important difference between season three and the first two years is that the third season producers did not have the money to "junk" stories and/or scripts that were not working out (page 399). I'm not sure of the veracity of this claim; certainly, the third season junked a few potential episodes, but it may well have done so less times than in the first and second season.