And here's my take based on what I've seen so far. Bear in mind that as the science progresses, the situation may change and the opinions I present may need updating.
Having years of expertise in applying biostatistical principles to clinical trial data in support of approval of novel therapeutics, I have been paying close attention to the recent early phase studies of the nCoV-2 vaccines currently being investigated. The first thing to understand is that to date, no confirmatory trials have been completed. All data that have been presented thus far have been from preliminary, hypothesis-generating/dose-finding studies.
Under the current accelerated approval pathway for these vaccines, it is entirely possible that a suboptimal dose may be approved for use, given our ongoing lack of understanding of how strong an immune response is needed to confer protective benefit. In other words, the earliest vaccines approved to prevent COVID-19 infection may be stronger than what is required to protect the individual while minimizing adverse events.
Second, only through large-scale confirmatory studies will we have a better understanding of the safety profile as well as the efficacy. Currently, I would say that the adverse events reported so far are generally a tolerability concern, not a safety issue. Having a fever or injection site pain, as long as these do not require hospitalization and do not generate long-term adverse health effects, would most likely be considered acceptable. The main safety concerns for any compound would be things like toxicity or organ injury. In this case, we would want to pay special attention to hypersensitivity reactions leading to injury. This is because there is evidence of a correlation between COVID-19 mortality and immune system hyperstimulation--the so-called "cytokine storm" that is treated with immunosuppressants to avoid damage to healthy tissues. And the high fevers that are reported as a result of vaccination is a possible sign of such a reaction, as well as potential evidence of efficacy.
Third, we have yet to determine the posology of these vaccines in relation to risk of infection, duration of response, and safety/tolerability. For example, some vaccines need "boosters," such as the HPV vaccine. Some are reformulated for each strain that becomes prevalent in a given season, such as for influenza. Some are administered once and that's enough to confer lifelong or nearly lifelong protection. Then the dosing of each injection is not finalized. Given that natural immunity arising from actual infection and recovery is likely to wane over a time scale that is measured in months and not years or decades, it is more likely that any successful vaccine will need to be administered multiple times in order to have sustained benefit.
I personally believe--and this is without any hard evidence--that an effective vaccine will not only cause adverse events such as fever, pain, and fatigue, but will need to do so, because these are signs of elicitation of an adequate immune response. Thus, the correct dosing and administration will only be determined with time. My main concern is that vaccine efficacy could be compromised as a result of incomplete adherence, noncompliance, and/or incomplete protection resulting in selection pressure for the virus to mutate. We have evidence that nCoV-2 is more easily transmissible than other respiratory diseases such as influenza; moreover, the existence of asymptomatic infection is another reason for concern for long-term control of COVID-19 through vaccination.
The bottom line is that it is still too early to be worried about the reported safety profiles from these small trials, because too much is still unknown, there isn't enough subject-years of exposure, and there isn't yet conclusive evidence of clinical benefit in the form of reduced risk of infection. We don't even have an estimate of the reduction in risk. The only efficacy data we have is antibody levels, and that is a surrogate for the real efficacy endpoint, which is the reduction in risk of infection as measured by a time-to-event analysis.