As a USA passport holder as well as a British citizen living in the UK are there certain things I may NOT invest in?
This is a highly specialised subject due to the different US requirements. So I would say that speaking to an adviser who specialises in this, would be the best idea. They will be able to give you a better answer than me.
All US passport holders have the requirement to file a tax return by the IRS (the US tax authorities) and all investments need to be reportable for US tax reasons.
There is a double tax treaty in place so you wouldn’t get taxed double, but the US want to know where all your assets are held.
A lot of the funds in the UK are not reportable in the way that the US would like them to be. Even things like ISAs are not seen as tax free for US tax reasons, so you wouldn't be able to invest in them.
Things which are reportable in the correct way are single shares held outside of wrappers (e.g. an ISA is a tax wrapper around your investments).
Pensions and the funds you invest in are not usually reportable in the US. So a lot of people take a view that for investing, they are fine in the UK.
NOTE: I would urge any US passport holders to seek full financial advice, to stop an angry letter from the IRS from coming their way.
Hope this helps.