I'm definitely glad to hear Agilent's trying to fix up their customer service situation after the whole failed firmware update debacle. I certainly understand that for the typical pro customer, human resources are more expensive and thus claiming "replace instead of repair" is a reasonable MO, but then it also seems like it's worth the few extra bucks to keep faith in the brand when things like this happen. I certainly don't want to be in 30 grand for a DSO7K series and have them dicking me around on repair costs and times, even if I'm more confident it'll get worked out in the end.
As for the display, I do LOVE the OLED indoors, and haven't experienced the fade (though I definitely don't use mine as much as you). The battery life is a huge loser, but if I'm inside I'm near the charger and other meters anyway, and if I'm outside, I'm not using the Agilent because the display is totally useless. Luckily, I don't ever need to measure things with 4.5 digit precision outside.
Of course, the ORIGINAL question was re: continuity, so I'll speak to that. People seem to complain that the Agilent's continuity detection is slow. That's fair, it is. But it's always compared to the 87-V, which has a much worse continuity mode. Here's why.
The way both continuity modes work is to measure resistance and sound a buzzer if it's below 10 ohms or something like that. The fluke is fast because it's sort of crippled, in a way: in continuity, it ranges to the lowest ohms range (600) AND STAYS THERE. So if you probe, say, a 1K connection, you won't hear a buzzer and the screen will display OL.
On the other hand, the Agilent uses its full ohms range, so if you probe a short, it'll autorange all the way from the top, which takes some time. It works out that it introduces a delay of a half second or so, where the fluke is more or less instant.
Here's the thing though: on the Agilent, you can simply manually range down to the lowest 50ohms, if you really need the buzzer to be snappy. On the Fluke, you can manually range UP to show actual measured resistance, but you can't set it to autorange in continuity mode.
I find it's more often the case that, on my bench, I have plenty of time for probing and the quickness isn't an issue, whereas I'd like to see what a value is if it ISN'T a short. For example, probing a power regulator, I can tell "these two nodes are connected" or "here's the top feedback resistor [as opposed to bottom]" in one probe, where with the fluke that'd be a PITA.
Basically, the agilent gives you the option, even if the default choice is the slower one. The fluke doesn't, so using continuity secondarily as a resistance measurement is annoying or impossible.