It was a discussion on more than anecdotal data. He also referenced this op-ed written by two doctors in the Wall Street Journal:
The database can’t say what would have happened in the absence of vaccination. Nonetheless, the large clustering of certain adverse events immediately after vaccination is concerning, and the silence around these potential signals of harm reflects the politics surrounding Covid-19 vaccines. Stigmatizing such concerns is bad for scientific integrity and could harm patients.
Four serious adverse events follow this arc, according to data taken directly from Vaers: low platelets (thrombocytopenia); noninfectious myocarditis, or heart inflammation, especially for those under 30; deep-vein thrombosis; and death. Vaers records 321 cases of myocarditis within five days of receiving a vaccination, falling to almost zero by 10 days. Prior research has shown that only a fraction of adverse events are reported, so the true number of cases is almost certainly higher. This tendency of underreporting is consistent with our clinical experience.
Analyses to confirm or dismiss these findings should be performed using large data sets of health-insurance companies and healthcare organizations. The CDC and FDA are surely aware of these data patterns, yet neither agency has acknowledged the trend.
Dr. Ladapo is an associate professor of medicine at UCLA’s David Geffen School of Medicine. Dr. Risch is a professor of epidemiology at Yale School of Public Health.
Are Covid Vaccines Riskier Than Advertised? - The Wall Street Journal - Newsfeed (newsfeeds.media)
(i didn't link directly to WSJ due to paywall)
Myocarditis and thrombosis are now well documented and listed as side effects by the CDC. Thrombocytopenia has also been reported and is being investigated.
This study generally refers to thrombocytopenia as a side effect of AstraZenica, but what i've read leads me to believe it will be applicable to some of the other vaccines (Pfizer and Moderna) as well.
No major safety warnings, other than rare cases of anaphylaxis, were reported in the initial trials, which involved tens of thousands of adults, and the risk of serious adverse effects has remained remarkably low after vaccination of more than 400 million people worldwide to date.1 It is not surprising, however, that new reports of adverse events have emerged as many additional people are vaccinated and follow-up is extended. For example, cases of immune thrombocytopenia and bleeding without thrombosis that were induced or revealed after exposure to the messenger RNA (mRNA)–based vaccines produced by Moderna (mRNA-1273) and Pfizer–BioNTech (BNT162b2) have been reported.2
The Journal has now highlighted three independent descriptions of 39 persons with a newly described syndrome characterized by thrombosis and thrombocytopenia that developed 5 to 24 days after initial vaccination with ChAdOx1 nCoV-19 (AstraZeneca), a recombinant chimpanzee adenoviral vector encoding the spike protein of SARS-CoV-2.3-5 These persons were healthy or in medically stable condition, and very few were known to have had previous thrombosis or a preexisting prothrombotic condition. Most of the patients included in these reports were women younger than 50 years of age, some of whom were receiving estrogen-replacement therapy or oral contraceptives. A remarkably high percentage of the patients had thromboses at unusual sites — specifically, cerebral venous sinus thrombosis or thrombosis in the portal, splanchnic, or hepatic veins. Other patients presented with deep venous thrombi, pulmonary emboli, or acute arterial thromboses. The median platelet counts at diagnosis were approximately 20,000 to 30,000 per cubic millimeter (range, approximately 10,000 to 110,000), but the rate of decline in platelet counts that preceded thrombosis is unknown. High levels of d-dimers and low levels of fibrinogen were common and suggest systemic activation of coagulation. Approximately 40% of the patients died, some from ischemic brain injury, superimposed hemorrhage, or both conditions, often after anticoagulation.
...
No thrombotic signal was detected in clinical trials leading to the approval of the ChAdOx1 nCoV-19 vaccine,9 which has now been administered to 34 million people worldwide. The incidence of VITT, as initially estimated, is perhaps 1 case per 100,000 exposures. This should be considered in the context of the incidence of cerebral venous sinus thrombosis in the general population (estimated at 0.22 to 1.57 cases per 100,000 per year). The initial focus of these reports may reflect a propensity to study patients with severe thrombosis occurring in unusual locations, and a more complete picture of thrombotic complications is likely to emerge over time. More information on potential risk factors other than young age and female sex is needed. Also needed are data on the prevalence and titer of anti-PF4–related antibodies in all vaccine recipients, especially those who had thrombosis at sites other than those commonly reported to date among patients with VITT, in order to apply Bayesian analyses to estimate disease probability on the basis of both clinical features and antibody titer in optimized assays. This may be complicated to achieve, because many cases of thrombosis that occur after vaccination are unlikely to be directly provoked by this exposure. Better understanding of how the vaccine induces these platelet-activating antibodies might also provide insight into the duration of antigen exposure and the risk of reoccurrence of thrombosis, which will inform the need for extended anticoagulation and might lead to improvements in vaccine design.
SARS-CoV-2 Vaccine–Induced Immune Thrombotic Thrombocytopenia | NEJM
Even The Atlantic has begun to acknowledge the seriousness of the side-effects of the vaccines, although it was an aside in an article about a non-vaccination treatment for Covid:
If the FDA sees no urgency, the Novavax vaccine might not be available in the U.S. for months, and in the meantime the national supply of other doses exceeds demand. But the asymmetry in coverage also hints at how the hype around the early-bird vaccines from Pfizer and Moderna has distorted perception. Their rapid arrival has been described in this magazine as “the triumph of mRNA”—a brand-new vaccine technology whose “potential stretches far beyond this pandemic.” Other outlets gushed about “a turning point in the long history of vaccines,” one that “changed biotech forever.” It was easy to assume, based on all this reporting, that mRNA vaccines had already proved to be the most effective ones you could get—that they were better, sleeker, even cooler than any other vaccines could ever be.
...
These two particular mRNA vaccines may have been the first to get results from Phase 3 clinical trials, but that’s because of superior trial management, not secret vaccine sauce. For now, they are harder and more expensive to manufacture and distribute than traditional types of vaccines, and their side effects are more common and more severe.
Hardline vaccine proponents continue to disregard any evidence that threatens their ironclad mantra that "the vaccines are safe". I'll be the first to admit, we don't know the real rates of the adverse effects yet, and it's likely that the rates for these adverse outcomes will be very low, but there's mounting evidence that these effects discussed above are linked to the vaccines.