I have done this on and off for a few years without any ill effects. Some positive effects have been better breath, cleaner teeth, I'd say also better digestion and immunity.
Usually I check this kind of stuff on earthclinic.com because they dont allow advertising products, people basically give feedback on various natural medicines, did it help them or not.
I also look up pubmed.gov for some science on it...
There are passionate claims that oil pulling helps with various diseases, especially autoimmune stuff. What is scientifically proven so far is that it helps with bacteria in the mouth and infections raging there, reducing bad breath and bacteria population. What I gather from all data available is that the improvement of various diseases by oil pulling has this basis: bad bacteria in our mouths, especially in the places that the toothbrush cant reach, like in between the teeth and gum pockets, small cracks in between the filling and the tooth (maybe root canals as well?), tax the immune system so much, that other illnesses improve - sometimes dramatically - when this problem is addressed by oil pulling. It is well known that people can get ill of rotten teeth and how it can cause all kinds of health issues. Lingual lipase is secreted during oil pulling, too, which might affect the body beneficially. I also believe that there is more to this, as with all the folk wisdom, than the science has currently caught up with.
Practicalities: some have experienced dental work getting loose, however, others claim that loose work will disattach and there is no problem if the fillings and crowns are well done. I'm in the second group, as for a few years I havent pulled any filling yet. I used organic coconut oil, and both refined and unrefined sunflower oil. I had no discoloration issues, in fact the teeth got a bit whiter. The reports of whiter teeth are mostly coming from those who pull with coconut oil. Traditional Indian oil of choice for this is sesame oil. Opinions are divided on whether it is better to use unrefined or refined oils. It would be best to try a few and see what gives the best result. It is important not to swallow the oil after swishing it for 10-20 minutes (not longer) because it contains toxins, and to well clean the tongue, not just the teeth afterwards.
Here are some links to scientific studies regarding oil pulling effects on oral health. They all agree that o.p. is a successful method to maintain dental hygienne and keep bacteria levels low. Skip to "CONCLUSIONS" section for quick scanning of what each study has shown.
https://www.ncbi.nlm.nih.gov/pubmed/18408265
https://www.ncbi.nlm.nih.gov/pubmed/19336860
https://www.ncbi.nlm.nih.gov/pubmed/21525674
https://www.ncbi.nlm.nih.gov/pubmed/21911944
https://www.ncbi.nlm.nih.gov/pubmed/25584309