I probably would. I generally go on the smell. DH wouldn't though - he is militant when it comes to BB dates. Having worked as a food buyer for a few years, I'm aware they're only a guide but he has none of it. He won't even use milk that's been opened, but that a seperate issue!
Sniff it and look at it. If it's gone soft and pale brown in places, and smells sweet or just 'not right', chuck it. A day out of date isn't reason to chuck it though.
What cut is it? I have thrown out in date chicken if it is in strips and smells sweet and rank, and minced beef if it goes light brownish or greenish before being out of date. Decent beef stored well should be fine, but you need to be able to trust your judgement.