:: This was it:
:: CREATE UNIQUE INDEX "IDX_Cart_1" ON "Cart"("InvoiceNo");
::
:: When trying to insert new rows and InvoiceNo was null, it
:: did this. Null is not a value - so why would this be a problem?

More info. This index was applied with many rows already having null. Ok -
but as soon as I applied this index, I could not insert rows any more with
null in that field. As soon as I deactivated or deleted the index - I can
insert just fine again.

Happens on both production and test DBs.