When measuring battery voltage, the tweezers will apply a 10mA load so you have a better idea if the battery still good or not.
Little known fact: If you swap the polarity, it does *
not* apply the 10 mA load, so you can get a quick check for whether the load makes a difference.
I keep an HP-4070C ($17 shipped, or a HP-990C, which is yellow but otherwise identical, $15 shipped) around at every desk. I think I use those more than any other multimeter. Doesn't do L, as mentioned.
I also have an MS-8911 handy (~ $50, harder to find but worth it), which can measure at 0.1 V (i.e., does not turn on silicon), so it is more useful in circuit, and measures ESR, but is pure LCR (no LED, battery, ... checks).
Finally, a DE-5000 (~ $100) for when I value precision over convenience.
(I also have one of the original Bob Parker ESR meters; those were the days.)
Oh, and a couple $7 transistor testers (both the 9 V naked ones, which I also use to build some special-purpose test rigs from, and the "LCR-TC1" cased version with Li-Ion battery, $13 shipped).
Not really useful once you have one of the HP-nnnC tweezers: MS-8910.
Looking forward to finding out how the DT71 will fit into this mix...
But did the scope image really show a 30 V peak-peak waveform?