Ok that's not looking too bad there. You can see the RC response at the higher frequencies.
You're not going to get a perfect square at maximum frequency on one of these. Even my 6 month old DG1022Z for example will only kick out a good square up to 5MHz as, due to Fourier's theorem (all squares are composed of sines at different frequencies), the thing would have to have 7-11x the bandwidth of the maximum frequency output to reach it (275MHz).
Here's a 25MHz square wave out on the DG1022Z connected to my DS1054Z as an example. This has twice the bandwidth of the HP3312A so I've shown it running at twice the speed:

I just referred back to the service manual instead of my brain as that's more reliable. The frequency response check (sine flatness check) is defined as follows so this is worth checking first. I've simplified this a bit:
1. Set output to sine, max amplitude, zero offset. Connect to scope via 50 ohm termination (your tee jobby should be ok).
2. Set frequency to 1KHz and measure p-p amplitude.
3. Set frequency to 100kHz and measure p-p amplitude. This should be within 3% of the reference amplitude from (2)
4. Set frequency to 10MHz and measure p-p amplitude. This should be within 10% of the reference amplitude from (2)
If this fails, something is up with either the measurement set up or the output amplifier. I'd suggest changing the measurement set up first. If it passes, you're good.
Also worth checking the output impedance:
1. Set output to sine, max amplitude, zero offset, 1KHz. Connect scope via straight cable.
2. Measure p-p amplitude on scope.
3. Attach 50 ohm terminator T/inline.
4. Mesaure p-p amplitude on scope. This should be approximately half of (2).
If that passes, it's probably ok. If it doesn't someone buggered up the output attenuator resistors. This is a common problem on these when previously owned by idiots. Look for burned ones on the board - they're pretty obvious and they cause most of the reduced output problems themselves:

Got to shoot out now for a few hours but will reply when I get a few minutes.