Fairly regularly on the 40m band I hear a quick blip of a tone, and when I look at the waterfall I see these brief transmissions all across the band that look like little dots. What is causing that?
It's probably an ionosonde — sending out HF radio signals not to communicate but to measure the reflections and thereby determine the current characteristics of the ionosphere.
The signal is probably not actually a series of brief transmissions, but a continuous chirp transmission with continuously increasing frequency. Two reasons:
As far as I know, this is how ionosondes work, and I've heard many chirps on HF, but never a stepped transmission.
If you look closely at the display, it appears that only one pixel in each horizontal line is lit by this transmission. If it were short bursts on single frequencies, we would expect to either see the transmission either taking up multiple pixels in the vertical time axis occasionally, or for some of the transmissions to be missed entirely, rather than a constant-ish spacing along the spectrum.
It looks like a series of dots because your waterfall display is displaying a series of momentary snapshots over time, not using the entire period of the signal between one line of the display and the next. (This is possible, but requires more computation. If it did, you'd see a continuous slanted line, but much more faintly than the dots because you'd be looking at the power effectively averaged over a longer time period.)
If this is a chirp, then if you catch the sound of it in SSB mode, you should hear a quickly increasing or decreasing tone, not a stable tone.
It appears from your photo that the pulses are not quite simultaneous; rather the transmitter sends a pulse, steps frequency up, sends another pulse, and so on. That behavior is what I'd expect from a propagation test beacon system, checking for things like MUF over a variety of paths and distances.
This kind of transmission would usually be received by a network of stations that would report back (by Internet, or before Internet via land lines or return radio transmission) on what frequencies pulses were received. This data, in turn, is combined with that from a number of other beacons and converted to an MUF path map.