They appear off centre but blued up correctly. I have a few 2 cavity moulds for moulding takeaway containers using open ended nozzles. I can't seem to get an even flow of plastic even after shimming, your help will be greatly appreciated.

It could be that your injection pressure or speed is shifting the core to one side. I have seen this before where the part starts to fill down one side faster than the other and shifts the core to one side slightly and one wall is thicker than the other looking out of round. You have to make sure all gates are the same size and all the walls are even. Try to use a program injection and start out filling slow so the material fills evenly over the bottom and as it starts to fill the side increase the speed from medium to fast. Good Luck!

If you add slight runner leads to the mold corners, the melt flow will drop over the edges and "PIN" the force piece. The melt FILL will progress down the sides.
This also takes the mold cavity (outside) and directs the melt flow.
Gate size balance and mold position. Also make sure the mold halves are centered.
Movable machine platent is square and mold clamp tonnage is balanced.

May want to use a reverse injection profile
1. "Low" first stage and
2. "High" second stage to complete the fill to final PACK

Bob has answered majority of your question, Try with higher MI material or higher clamp force. Also please check the the top plate and back plate thickness.

We too have 2 cavity thin wall container did not sucess , havine same problem mould does not balance.. good luck

Thanks guys, it's really nice to know there are helpful and caring people like you out there in this day and age :)

The halves were blued up and seem fine, but I'm thinking that it's possibly the contact plates that are worn, the moulds are 6yo and very neglected by previous owner.

I have tried reverse fill profile and surprisingly it does work!!! But only for 1 cavity, slight adjustment to fill the other cavity and then the other side flashes, turn the heat up on the cavity not filling but not much change.

It is a consistent problem, ie the flow is always in the same spots, not much cooling either to eliminate cold spots.

I only have a few hairs left on my head, so I have tried most things, any other suggestions?

Mold Height distance is critical between the Cavity and FORCE,
There may be a difference in Mold Height and variance in BAST thickness determines which fills FIRST and PUSHES the MOLD OPEN.

better check the bearing / bush for your injection machine as well. sometimes it may not the issue of the mould only.

I just tried another mould and the exact same problem, between the 2 cavities is where the plastic doesn't flow, checked cooling and appears even, could it be the machine? It is a cheap Chinese machine using toggle clamp :(

Have you checked the machine nozzle orifice?? If it's too small then even with reduced injection pressure there is still high pressure which then produces a lot of gassing, check the vents along the parting line to see if they're clean, maybe even increase the venting, you could also try putting some tape along the parting line to intentionally hold the mold open to see if the flow improves,

I would play around with your tip temps, mold temp and injection rate to see if you can get some settings that work. Start with a warmer mold, warmer tips (tweak each one independently to try to get equal balance between cavities, don't worry if one is 20-30 degrees C different from the other at this point) and slower injection rate. You'll take a cycle time hit but you might get full balanced cavities without flashing and can optimize from there.
If your machine is a cheapo you might not have enough tonnage to keep the mold closed during filling for these thin wall parts. That could explain the core shift and flashing.