you have the classic door leak and until you get that sorted you will continue to have issues.
It reads like you need to do the mod/repair on all doors.
the photo shows the door card seal has broken down and is leaking. V common. search on here for leaking doors and you should find loads of info.
see here >>>>> seatcupra.net/forums/showthread.php?t=44216
EDIT: even better now with pics here: >>>
http://dubsteve68.blogspot.co.uk/2011/05/seat-leon-leaky-door-seals-repair-guide.html
I have done a good few doors and can get them done (properly) in about 30 mins for each door. Figure 60 mins - 90 mins for your first door as you learn
how to remove trim and how its done etc. my tip, take some good time to clear out the old rotted seal and also get some alcohol wipes etc to clean the surface before fitting new seal.
oh yes and depending on what seal you use, if its too sticky to handle easily (it will be in hot weather) stick it in the fridge for a bit before use to make it more usable.
It may be the carpets don't appear wet but you may have lots of moisture in the car, if the underlay for example gets wet underneath the carpet you will have issues.
I do agree the pollen filter is a potential issue too, - you will tend to find the windscreen at the bottom of the passenger side gets effected more so in that case.