As a reader, I want to feel that the author knows the period at least as well as I do, and preferably better. I hate it when the author makes historical blunders that could have been avoided by ten minutes of the most basic research, or when the characters are plainly twenty-first century people thinly disguised in historical costumes. Dialogue that is too modern takes me out of the story, but clumsy attempts at period dialogue (tortured syntax, weird use of vocabulary) are even worse.
What she said. Especially the bit about twenty-first-century people. One thing that irritates me no end is all these feisty females who defy convention, yet somehow never have to suffer the consequences, not even a little bit. Apart from anything else, it makes their defiance much less a demonstration of their own strength of will: after all, they haven't had to risk anything. Makes you wonder how stupid and lazy the author thinks all the other women are, if defying convention is as risk-free as all that...
I also remember reading, or possibly speaking to an author, about writing Roman fiction - the difficulty of writing a protagonist who was convincingly Roman, yet still acceptable to modern sensitivities (what with the slave-owning, and the conquering other countries with fire and sword and all that). So you tend to see a lot of republicans who own a couple of slaves but make poor purchase choices and feel guilty about it.
Personally, I think attempts at period dialogue are worse than the author just going for modern syntax. I tend to assume that the speech should be mentally translated to whatever is appropriate - so Lindsey Davis's Falco in first-century Rome talks like a 1930s noir detective, and that fits - and it gives you an instant feel for what Falco is supposed to be like: a PI who's tough, honest, down on his luck, and a sucker for a pretty girl. Back in Rome, I there was probably an equivalent tone, but in Latin, and I assume that that's what Falco is 'really' using.
As for deviation from the historical record, for me - as little as possible. It's always a disappointment to find that an author has moved things around for plot purposes, especially when there's so much history just lying around for the taking, with all sorts of good bits. To go back to Lindsey Davis again, her first Falco novel (the Silver Pigs) [currently on offer at £1.99!] features some lead ingots. The ingots are real, and were found by archaeologists - and the fact that they
had been found by archaeologists meant that fictional Falco had to leave his fictional ingots for real archaeologists to discover... Thus demonstrating Davis' faithfulness to history, or at least to causality!