As is well-known, the ten-frame buffer window only allows you to buffer a single input at a time in Smash 4.
That said, there appears to be a set priority for inputs done within the normal ten-frame buffer window, regardless of the order buttons were pressed: Special > Shield > Attack > Jump. This was tested out of airdodge, knockback that doesn't put you in tumble, knockback that puts you in tumble, and tumble. At first glance, here's how I think this appears to affect the metagame:
Very weak attacks that put the opponent in the air after hitstun (things like some Jabs, Mac N-Air, etc.) tend to turn complex inputs (as in, involving more than one button) against the user. Reflexive shieldgrab inputs turn into an airdodge, giving you a pretty big window to punish. You can't buffer a jumping aerial or special, either, so in order to jump away from the situation, you have to be relatively passive, which may be useful for the attacker trying to follow up.
Also, buffering jump-cancel out-of-shield options is made slightly harder (though it was already super-hard due to being unable to buffer two inputs at once), due to Attack having priority over the Jump button. This is why if you press Attack while in shield hitlag and then press Jump, you'll get a shieldgrab; the game still wants to buffer the Attack input.
Some quirks: A+B Smash makes it so that pressing Special while also pressing Attack (either at the same time or by pressing Special while holding Attack in advance) turns the Special input into another Attack input instead. Also, you can airdodge out of the end of knockback that would otherwise put you in tumble, so input priority doesn't matter in that situation (since all other inputs do nothing in that instance).