No ,There will not be any side effects of the extraction. Not on the overall health, but there can be complications which is very rare .surgical extraction have slight increased chance of complications .100% gurantee cannot be given for any thing .even a small medication that you take for a cold has side effects .as far as post extraction care is concerned. You may have to be a little cautious for a around 4-5 days about the wound
that is all take rest for one day after the extraction. The amount of care needed will be told by your dentist
depending on the type of extraction ,if it is a surgical one you need to rest for probably 3 days. If your tooth is broken and stays there it may cause pain and infection
or even swelling
so I suggest you to get it removed. Hope this helps.