Different tyre size combo, 23 fr 25 rear??

I'm running 23 up front and 25 at the back but only because i shredded a tyre the other day and the spare tyre I have is a 25mm. I've had 1 ride so far and had no issues, other than the colours don't match (these things are more important than rolling resistance and comfort).

A 25 on front is more aero - no?

That's what I'm running at the moment Michelin pro 4 race 23 front pro 4 endurance 25 rear. Reason for this is the rear tyre needed replacing and wanted to try a 25. Defo like the 25 rear am undecided whether it would make any difference on front

There's nothing wrong with it, I did it for a season. Slightly lower rotating weight, smaller frontal area but marginal at best. If you're very light then taking into account that there's less weight on the front you can start to get down to pressures below the recommended minimum running wider tyres, if you use e.g. Sheldon Brown's calculation method. So narrower can help. Now I run 25 f&r with equal pressures with no ill effects however.

If you run odd sizes you won't be able to rotate tyres front to rear when the rear wears out first of course.

I was using those 22 mm and 24 mm Contis on one bike but they wear out pretty quick so I thought I would try 23 mm GP 4000S on the front and 25 mm on the back, on my other bike. It works fine, I don't need any extra comfort on the front but it's good at the rear. I have never tried a 25 mm on the front though, so don't know if 23 mm is any better apart from a possible slight aero advantage.

Continental sell twin packs of tyres for this purpose, but theirs are 22mm up front and 24mm at the rear. I think they have different tread patterns as well.

Can't think of any real advantages to be honest - an insignificant aero difference maybe, perhaps marginally less (or more) chance of pinch flats depending on rim size, probably less leeway to get a more comfortable ride on the front, a tad less grip. If I was a betting man i'd say there's possibly more cons than pros - but it's not by much either way. I'd go with the 25s FWIW.

Nah, I'd say 25 all round for better comfort, rolling g resistance and handling.
Having a 23 front may be marginally more aero but such a little difference it would be unnoticeable unless doing very accurate testing...