This article from 2009 discusses using the valsalva maneuver while weightlifting. The big caveat I can find after a quick scan is that the maneuver has cardiovascular risks when used while lifting weights, especially if the weightlifter has higher blood pressure already. The big risks are increased blood pressure, increased heart rate, and a risk of cerebral hemorrhaging. It also seems that the maneuver is only really beneficial (and somewhat natural) for certain exercises and when attempting a maximum rep. However, the paper recommends a forced exhalation should be used to mitigate the above risks.
Thanks to @sagnick das in the comments for prompting the following: Another article (Behind a paywall but relevant info summarized on this NSFW page under "Pelvic Pain in the Athlete") states that the maneuver can cause/exacerbate inguinal hernias, a condition that can also happen due to weightlifting (also stated in the article). Disclaimer: I did not dig deep into this article due to the NSFW content and paywall.
There seems to be some benefits to using the maneuver, but outside of strength training. Most notably, and the only time I've purposefully used it, is attempting to treat supraventricular tachycardia.