A multimeter can make it look like a chip is receiving the correct voltages, but there can be all sorts of noise and fluctuations that will cause really strange and inconsistent issues. You don't need a super fancy scope, even a 100mHz cheap handheld is more than good enough for checking power rails.
Also, for anyone who has to troubleshoot or fix boards, those smd resistor and capacitor kits are absolutely invaluable to have on the bench. After a decent scope, meter, and soldering station I would say that should be the next purchase for setting up an electronics lab. Nothing more annoying than trying to debug an issue and having to wait for the right value cap to be shipped. Especially since capacitors specifically often seem to have some trial and error to finding the right value for something like a decoupling cap. Fully modeling the noise generated on a supply rail often isn't completely possible, at least in my experience.