Fiber without water is the worry more than fiber. Stuff like thick oatmeal without enough water can clog you up good. But fiber overall is more likely to help prevent diverticulitis. A lot of fiber is ingested with enough water(fruits and vegetables for the most part have high water content) that it speeds through very quick.
The two main problems with fiber is it moves really fast through your system and that can take a while to get used to, especially if you eat heavy meals and don't drink a lot of water. Discomfort and gas can result, which nobody likes. And also, it can absorb vitamins and minerals. So, as another poster noted above, you might want to take vitamins at a different time than eating especially high fiber foods or supplements.
After a short while, someone on a high fiber diet can get used to it and not be gassy anymore. I eat a huge amount of vegetables and fruits and find I'm less gassy than I was when I ate less of them. Drinking enough water and eating flax oil and omega-3 oils and the other oils people at T-Nation recommend can help keep your meals passing through your system quickly, so a fiber meal doesn't act like an irritating plunger trying to force your enormous stool down a dry intestine.