Maybe others with a few kilometres on their manual GP have found a problem shifting, particularly into 1st gear. A few probable causes have been discussed on this forum and beyond but I have just gone through a few processes that might be helpful for anyone new to the problem.

1 Hydraulic clutch bleed.
The first issue seemed to be a very deep clutch point, so I went to adjust the clutch cable and found there wasn't one. There is (luckily) an hydraulic clutch that automatically adjusts itself - but only when there is no air in the lines. The clutch shares fluid with the brakes. First, bleed all the brakes at each wheel until you are rid of all the old fluid (general rule, rear left wheel first? I've forgotten, so google it). Then find the bleed nipple on top of the clutch slave cylinder. Stick a clear tube on it and stick the other end in a clear bottle on the ground under the car. On my 2008 1.3 JTD there was no nut on the nipple and I needed to release the attached hose and back it out 5mm and then fluid could flow freely out. I used a pressure bleeder to blow air into the brake fluid reservoir, compressing brake fluid through the lines. (You could use another method.) I found the best result came from an idea I got on a Porsche forum; I pushed down the clutch pedal with a piece of timber about 70cm long and held the clutch pedal down by sliding the driver seat forward to hold the other end of the wood. With the clutch master cylinder compressed there is one less hiding place for air bubbles, which can then be drain with the fluid. I ran through a whole 500ml bottle of DOT4 brake fluid to bless the clutch alone. Make sure to keep refilling the fluid reservoir so it never runs dry during the process. Make sure you rescued the hose (to close the bleed nipple) before releasing the clutch pedal. Doing it with the cliche compressed gave me a much more define clutch movement (than when I first bled the slave cylinder without the compressed clutch pedal).

2 Gear selector cable adjustment.

If you find that you are not quite getting into certain gears, check that your cable lengths are correct and adjust them. I'm sure the manual has more exacting procedures but my rough method was this. Drive the GP up on ramps and chock the rear wheels and pull the handbrake on hard. (If your handbrake cable is too slack, adjust it so you have a solid handbrake.)
Get under the middle of the car with a large flat screwdriver and locate the plastic hatch that covers the gear lever mechanism. Use the screwdriver to ease the clips out of the recesses in the plastic gear lever mechanism box. Have an assistant change gears and see whether and where the white plastic halfway down the bottom end of the lever contacts the edge of the plastic housing. Pop the bonnet and using two 10mm spanners, undo the locknut on the gearbox end of each connector, use the large screw driver to 'pop' the ball joint off, and then use your amazing brain and your assistant's help to adjust the length of the cables so that when selecting each gear the white disc does not foul on the housing. You will find about 5mm clearance in front back movement and only about 2mm left to right. Make sure to do up the lock nuts and you can try to make the ball joints sit flattish but it is very tricky and I'm not sure it will improve the life of the parts anyway. Doing this with new cables I found the adjustment to be perfect so it should work with old cables.

3 Broken gear selector cable
If you (like me) are lucky, one of the gear selector cables will snap while driving. This is particularly hilarious on a bypass road at 80km/h at 4:30pm on a Friday. So you call up the dealer and give them the part number for one of the cables. In my case I was told there was only one available in Australia (in Melbourne somewhere) and would cost over$300, and the other would need to be sent from Germany and would cost over $400. So I bought both cables for 1/10th that price with a bunch of other spares from shop4parts and these parts arrived very promptly. It being Christmas time I finally got to the job after everyone had taken holidays and after removing a cable found it had a clever plastic clamp on the gearbox end that is removed by inserting a flat blade screwdriver in a slot and turning, and a pain in the arse plastic barbed clamp at the gear lever end that needs a special toll or (in my case) destruction for removal. Then I found that the parts I received had a simple metal clamp body on each end with two slide in clips. I called the supplier but they were on holiday. Our second car, the Land Rover decided to cover itself in coolant the same day and so I had no car to even get to work Monday, let alone for my wife to use. Then suddenly It became necessary to pick up a family member from hospital the next day. So it was do or die. I found that these parts could fit my GP and work well. To fit them at the gearbox end was simple, as the clamp bodies can just be dropped into the flange on the gearbox and the clip can only be inserted on the backside of the flange (away from the cable end). The gear lever end required modification of the clips. Straighten the two tines and the twist them inward about 30 degrees so the can slide over the plastic reinforcement in the gear leaver mechanism box. To be honest I would prefer to have the correct parts, but I don't have time or money to follow it up. If you do get hold of the cables with the plastic clamp bodies the install should be very quick. I didn't remove the battery to do this, but stood on my Land Rover spare wheel I laid out in front of the car to get height from which to insert both arms into the back of the engine bay. Long sleeves would have saved me some scratches but after three beers I didn't care.

I can post pictures if anyone is interested in trying these procedures.

Please

If you would be so kind post them in the grande punto section in the guides
https://www.fiatforum.com/grande-punto-guides/

Just came across this thread. Would love to see some photos. Thanks!

Please post pictures then

Pictures would be a good option

I would be like you since I've had a gear selector cable snap on me. Stuck in 2nd and had to drive back in 2nd. Battery shorted out after this. £600 total repair job