I can hear:

Bass line (it's there, and it's sort of independent, but it's not that interesting)
Keyboard elements - lots of filled out harmonies and a couple of extra lines
Backing vocal harmonies - quite complicated
Extra guitar lines - one part where it plays a very simple line which is mostly a held note and some embellishments
And more...

Most of this is already happening before the bass and main drums come in at around 18s, and you could easily spend some time playing that section over and picking apart everything that's on the track.

There's a surprising amount going on - as there is in a lot of chart music.

People tend to remember the melody line and aren't consciously aware of the rest, so they'll either not hear it at all or hear it as filler. But listening to it can be - interesting.

Also interesting that you don't like the beat. Caroline Corr often seems to drag the snare beat slightly and make it late. It's probably my least favourite thing about the band.

Meanwhile ¨Try whistling this¨ is a bit of a cheat. I'd hear it as:

Voice melody
Piano countermelody (which sometimes disappears)
Piano harmony and colour around the countermelody
Occasional embellishments and decorations

You couldn't whistle it because a lot of the movement and interest is in the countermelody, hidden under the sung part which is simpler and not as interesting - as you can hear when he stops singing.