I have just bought a 2008 Fiat Grande Punto 1.4 t-jet with 88,000 miles on it.

Are there any common issues I should be prepared for?

The brake light switch on the pedal is known to go, which will translate to lighting up ABS/ESP on the dashboard the first time you brake. It's an easy replacement.
Also, the door latches are known to make creaking sounds on uneven terrain. The remedy is to use a bit of lube on the latches and the creaking will stop.

I haven't got experience with the engine.

Check for rust at the brake servo due to leaking seal above :

https://www.fiatforum.com/grande-punto-guides/241678-fix-water-footwell-rust-brake-servo.html

Also check for weird electrical malfunctions in the tailgate - the wiring loom (top left corner of the tailgate recess as you look into the car from the back) can fracture. I had to solder all of the wires AND repair the washer fluid tube on Wifey's Punto

This is interesting Nigel, the number plate light is out on mine. The only other thing is the front brakes squeal. I am taking it for a free brake check on Tuesday. It has a 3 month guarantee so hopefully I will find any problems by then.

I absolutely love the car. It's really quick, and very practical for my doggies. It's also beautiful, in blue metallic with shiny alloy wheels. It has helped me to feel less sad about parting with my Coupe.

My wife often took our dog in her Punto. He’s a 13-stone Newfoundland- he touched both sides at the same time!

Congratulations on your purchase Annie. We had a Grande Punto 1.4 8v of a similar age until 2+ years ago when we upgraded to a 500X. Our Punto was red, but I do like the metallic blue, much better than the white.

Had no problems with ours but the 8v engine did lack power on the open road, which you won't have with the TJet. Plenty of room in the back with the rear seat down for your dogs and/or travelling.

When I realised the Grande Punto was designed by Maserati, I knew at once I would like one! I did a bit of research and decided on the 1.4 t-jet. Then it was just a question of finding a good one. I got as far as putting a deposit on a local one, before finding out the rear suspension was shot and the MOT was dodgy. I managed to get the deposit back but only by getting very cross and mentioning trading standards. Then I saw this lovely blue one on Pistonheads, being sold by Evans Halshaw in Wolverhampton. It was such a relaxed and enjoyable way to buy a car, although I have never before met a used car salesman who knew so little about cars. He didn't even seem to know what a cam belt was! I have put a dog hammock on the back seat for Moss, and Snoop travels in the boot area with the parcel shelf removed. I am now going to sit back and enjoy the spectacle of my neighbours buying a new car, as they always do when I do! Some people!

My Coupe is for sale on here and on eBay. I hope I might own another one someday.