Flue should run uphill so condensate runs back to the boiler. You still get occasional drips from the flue outside but it should never be much more than a few drips now and again.
You should be able to see it but it will be very slight!
Look at it from the side and you should see it. I think from memory it's a 3degree incline minimum.
I would only worry if you are watching regular consistent drips.
Have a look and see if you have a plume deflecor as well.
It should be on the flue at the very end. It should have a screw which can be adjusted so you can twist the deflector to direct the plume in a chosen direction. I have had a case where condensate was getting trapped in this fitting and dripping from that.
Try directing it upwards (if not already)
I would consider getting the installer back in any case!
If this one has a built in slant then horizontal is ok. Just make sure it's level in this case. 3 degrees isn't a lot and if it's not spot on level maybe it's lost the slope.
I'd check the deflector and make sure it's at least level as stated. I tend to go a little more than spot on level anyway even if it's built in!