Are there food safety issues with sous-vide cooking?

If you do it properly, no there are no health issues.

A combination of two things are required to kill beasties: heat and time. The higher the heat you expose them to, the faster they die. Generally any temperature above 130 F is enough to kill most beasties, it just requires a significantly larger amount of time compared to a higher temperature.

I go into a lot of detail regarding Salmonella in this answer of mine:

Is it safe to eat a cooked steak that (briefly) touched the plate that was holding the raw meat?

I have several tables there to show exact timings, etc.

_{If you think I should copy/paste that here, then let me know in a comment}

There are a couple of things to consider when cooking sous vide in terms of safety:

1. What is the time and temperature required to kill the nasty stuff present in any given piece of food. There will be a minimum temp and time for anything and it's highly dependent on the thickness of the meat.
2. Some sous vide preparations don't get to those minimum times and temps. This is generally preparations of fish. In this case, you should use sushi grade fish and not serve to anyone who is immune compromised. Think of it as the same as eating it raw. If you follow the same safety guidelines, you'll be fine.
3. Since you're cooking in a vacuum, botulism can be an issue. All food should be cooked within the recommended cooking time. Food should either be served immediately or flash cooled in an ice water bath and then kept below 38F in a fridge for 3-4 weeks. Home fridges are generally not good enough to keep the temp below 38F, so this shouldn't be done outside of commercial grade equipment.
4. Cooking times should either be kept under 4 hours or be sufficient to achieve pasteurization.

Douglas Baldwin has produced an excellent, free resource, A Practical Guide to Sous Vide, that goes in to great length on all the safety concerns. It also lists general minimum time per temp per width for different cuts of meat and discusses when you can ignore those and what the additional risks and considerations are.