[James2001]

It's ridiculous just how many clock designs there were in those last few years, especially when the first one managed to last unchanged for half of the show's run! Then it kept changing every few months.

[Brekkie]

That was pretty much the same for most elements of the show.

[eggsontoast]

Very unusual, especially with the odd colour scheme and showing the wrong time. It appears at the same time as the other clock, so clearly generated by the same piece of kit. Obviously wouldn't have been seen on air because, as you said, the actual BB2000 branded clock would be covering it up, but it's strange nonetheless. Looks like someone does notice and fades it out after around 3 minutes.

Didn't they go back to that style of clock (in the proper colour scheme) after dropping the BB2000 branding, or did they move to something else? The style of clock changed so often in that era that it's hard to keep up.

I'm gonna take a guess at this. The normal time of day clock was produced by a dedicated "Miles Clock Generator", it was completely seperate to the Inscriber machine which produced the lower thirds etc.
On the Brekkie it was commonplace to play timer graphics in off tape. So I reckon the countup clock had been prerecorded from the Inscriber after the previous days show on a chromakey background but accidently with the Miles clock generator still on the vision mixer output as well.
When this was played in the next day the clock is slightly keyed out being too close to the chromakey hue and hence the time being wrong.

[James2001]

Though that doesn't explain why it was a previous clock design which had stopped being used by this point.

[eggsontoast]

Though that doesn't explain why it was a previous clock design which had stopped being used by this point.

Think of these clock graphics as being targa image files, or in some cases targa sequences that run on LTC timecode. If the BB2000 sequence had only been rendered between 6.45 and 9.15 then after that any old stuff previously stored would show before and after that time period.