OK, I'm fed. For now.
Looking at the wiring diagrams on pp. 63-64 of the datasheet, and the internal ADC block diagram on p. 561 of the Family Reference Manual (http://www.ti.com/lit/ug/slau144j/slau144j.pdf), it looks like chip-to-board ground differentials could indeed be the source of your problem. It also looks like there might not be a darned thing you can do about it.
The way I interpret the block diagram, the 2.5V reference voltage probably is generated relative to internal AVss (it's hard to tell; they show the ref generator going to a ground symbol, without specifying which Vss it is). If you're using that internal reference, that means Vref+ is +2.5V relative to that point, not +2.5V relative to circuit board ground. So how stable the ADC reference is, is therefore partially dependent on how much that internal AVss bounces around. That might be only a little, or it could be a lot; I have no way of telling.
One investigation you could do would be to take a look at the Vref+ output from the chip using a good scope set for AC coupling and a vertical scale of 10mV/div or thereabouts, and see if you observe any fluctuation as the μC goes through its paces. That might yield a clue: if you see absolutely no bouncing around whatsoever, I'd say chip-to-board ground differentials are probably not what's causing the problem. If you do see Vref+ wiggling up and down, they probably are-- but in that case, I suspect you're out of luck because I can't see any way to correct the problem without resorting to an external, stable reference.
JohnInTx and nsaspook might have different angles on the problem, but that's my take.
I am definitely NOT a fan of voltage references on μC chips, because of exactly this problem. They're OK for crude, low-precision work, but when you're trying to squeeze a full 12 bits of accuracy out of an on-chip ADC, those built-in voltage references fall far short of the mark. (I noticed on the datasheet that the voltage reference has a tempco of up to ±100 ppm/°C; that means with a 12-bit ADC, it can drift as much as 1 LSB every two degrees. Not good!)
That's all I have for now...
Looking at the wiring diagrams on pp. 63-64 of the datasheet, and the internal ADC block diagram on p. 561 of the Family Reference Manual (http://www.ti.com/lit/ug/slau144j/slau144j.pdf), it looks like chip-to-board ground differentials could indeed be the source of your problem. It also looks like there might not be a darned thing you can do about it.
The way I interpret the block diagram, the 2.5V reference voltage probably is generated relative to internal AVss (it's hard to tell; they show the ref generator going to a ground symbol, without specifying which Vss it is). If you're using that internal reference, that means Vref+ is +2.5V relative to that point, not +2.5V relative to circuit board ground. So how stable the ADC reference is, is therefore partially dependent on how much that internal AVss bounces around. That might be only a little, or it could be a lot; I have no way of telling.
One investigation you could do would be to take a look at the Vref+ output from the chip using a good scope set for AC coupling and a vertical scale of 10mV/div or thereabouts, and see if you observe any fluctuation as the μC goes through its paces. That might yield a clue: if you see absolutely no bouncing around whatsoever, I'd say chip-to-board ground differentials are probably not what's causing the problem. If you do see Vref+ wiggling up and down, they probably are-- but in that case, I suspect you're out of luck because I can't see any way to correct the problem without resorting to an external, stable reference.
JohnInTx and nsaspook might have different angles on the problem, but that's my take.
I am definitely NOT a fan of voltage references on μC chips, because of exactly this problem. They're OK for crude, low-precision work, but when you're trying to squeeze a full 12 bits of accuracy out of an on-chip ADC, those built-in voltage references fall far short of the mark. (I noticed on the datasheet that the voltage reference has a tempco of up to ±100 ppm/°C; that means with a 12-bit ADC, it can drift as much as 1 LSB every two degrees. Not good!)
That's all I have for now...