There's no problem with eating tomatoes. Just remember that they are not a sweet fruit and so are not included in the 80% carbohydrates (80/10/10). They are generally eaten at the end of the day along with tender leafy greens and overt fats.
For the record, I eat tomatoes pretty much everyday of the year. :)
Tomatoes are part of the nightshade group of foods which may pose problems when eaten in excess depending on different factors. (I recommend researching nightshade foods.) It can aggravate some conditions like arthritis so severely that sensitive people will feel a reaction from eating any nightshade foods.
I will back up leafygreen's statement. I've read research (living with lupus is a great book for some background on the disease and they have pretty good recommendations on which products and foods to avoid) and have experienced the phenomenon (prior to reading the research actually..but it explained a lot). I stay away from tomatoes, potatoes, eggplant and peppers..but I miss them :( If I eat tomatoes, my eye sockets swell and it's pretty painful. I can usually get away with potato, but I don't eat cooked and if I do eat much my joints hurt, so I just focus on the foods that don't leave me feeling gross the next few days.
Most people can eat them and feel great though, so it just depends on what kind of health stuff you are dealing with.