Leaky gut basically refers to damage that has been done to the lining of the gut due to pathogenic involvement.
The gut is a very complex environment made up of many strains of beneficial bacteria and the like. The gut also makes up a large percentage of the overall immune system with such things as Peyer's Patches. If you would like to read more, I would suggest googling 'Dr. Leo Galland', he has some great resources.
There are a multitude of different pathogens that can inhabit the gut such as bad bacteria, yeast/fungus and parasites (worms, protozoa and perhaps some species of flukes).
If you suspect leaky gut then proper testing is the only way to go. Metametrix GI Effects test (panel #2105) is the only test recommended due to their advanced testing (PCR). I see too many people attempting to treat things they think they have. And if you don't know what you have, then how are you going to treat it? For instance treating rogue bacteria is different from treating worms which is different than treating protozoa.
You can attempt to rebuild the gut lining with a number of products, probiotics included. There are a number of products that can help such as colostrum, aloe vera juice and proper probiotics (I like Jarrow EPS for several reasons).
Cleansing may be another good option. The gut is one of the important things to cleanse and rebuild.
I have never heard of someone having a negative reaction from using probiotics unless it was rancid or contaminated. Do you have a source for this story?