Do you think this vaccines will cause other health problems down the road?

Why do you think it would do that??

Pointless speculation on absolute unknowns. 

Not nearly as many as Covid will for those who contracted it.

I think they might.  Here's a better question:  Why do you care what random strangers think?

There are teams of medical doctors looking into that very thing as we speak, and they don't have any idea.  Do you really think online strangers know the answer?

COVID-19 has killed 553,000 Americans and counting.  This is greater than the number of Americans who died in WW 1 and WW 2 combined.  Over half a million COVID deaths in America alone is the SIDE EFFECT OF NOT GETTING VACCINATED.  We should be grateful that we have access to the vaccines!

No way to know for sure until time passes.  There is no evidence of that yet.  

Probably not, but I'm not taking that risk against a virus that has a >99% survival rate.

There's not a lot of mystery about vaccines.  Vaccines have been around for more than 200 years, and more than 10 billion vaccines have been administered in that time.  Patterns with adverse side effects are well established.  There have been a few vaccines that have gone wrong for various reasons and those problems were not repeated in later vaccines.  Most of the people that have serious side effects have medical issues that make them susceptible. On average, vaccines cause serious adverse effects in around 3-5 people per million vaccines.  That will probably not change in the foreseeable future.  

Possibly but it cannot be any worse than dying on a ventilator.