Long-term effects can only show up in the long-term. The UK has won the Pfizer race but Russia and China already won their own races. The EU and the US are just slow (but claim credit for a prudence that is not possible). They are both so heavily invested that they cannot not approve. In fact, the world needs the vaccination initiatives to proceed with all speed, no matter the immunization conferred. Deployment of their own vaccines has started in Russia and China and the Pfizer vaccine will start being deployed in the UK next week. Other countries will follow – have no choice but to follow. The low cost vaccine is the Astrazeneca / Oxford vaccine which is probably 2 months away. Some few countries will deploy the Chinese and Russian vaccines. 2021 is vaccination year. It remains to be seen if this succeeds in preventing another Covid-19 spike in spring 2021.
Long-term effects are unknown but unlikely. The period of conferred immunization is unknown and will come out in the wash.