Looking at the tiefling building options, and I'm wondering about the value of the Fiendish Heritage feat.
For a roleplay oriented campaign it matters little, as mechanics are mere crutches and the loss of a feat is less of an issue. But for the average game that tends to be more stat oriented, why would someone wanting to play say a cleric, pick a race where they might not get a wis bonus (or even might get a wis penalty)? Alternately (using Fiendish Heritage), why would they pick a race that has no real advantages over other races, but gets hit with the disadvantage of no usable feat at 1st level? Most character generation methods allow you to arrange your rolled stats to fit your character, and even point buy lets you get a controlled, predictable output, so this randomness (or feat cost to eliminate it) doesn't make sense.
And with the chart to pick a trait, I've done practice rolling just to judge the value, and rolling once or thrice matters little, character changing traits came up extremely rarely.
While some traits are pretty powerful if allowed to pick outright (heirloom weapon, oversized arms and a huge bastard sword, suddenly you're doing 3d8 base damage at a mere -1 to hit, or alternately an extra +2 to your prime casting stat as a caster), I don't feel that 3 rolls on the chart gives you enough of an advantage over 1 to justify the feat. If I were to DM with the variants allowed, I'd just say pick your variant, roll once for your trait (treat it as flavour, don't expect it to be a significant part of your character's mechanics), and don't bother with the feat.
D&D has been steadily moving away from randomization of character abilities, and I think there's good reason for this. It's nearly impossible to make a large table like the tiefling table well-balanced, and random rolls on a non-balanced table tend to lead to frustration in the player group.
I would use this table only for NPCs. Either allow players to pick what they want, or don't use the table for PCs at all.
We had a very specific party conception--most of the PCs were blatant tieflings, but one was a human-looking tiefling who was the "token human" in the noble house. For that to work we had to pick, not roll, and that has seemed to work out fine. Being human-looking is essential for Lady Varuna's political career but it's also a constant worry for her--if she is ever found out, blackmail is inevitable. She's had to grope around in the dark pretending not to have darkvision from time to time, and worries that she'll get caught on the fire/cold/electricity resistance or the spell immunities.
If you have tiefling PCs, incidentally, the GM needs to think about the implications of "type: native outsider". This should technically mean that charm person, hold person, dominate person, enlarge person, and reduce person do not work. However the modules do not follow this rule: they show successful use of charm person on tieflings. It could work either way, but the GM should pick one and be consistent. (Actually this is important even without tiefling PCs as there are lots of tiefling NPCs.) We chose to have the spells not work, which has both helped and hindered the PCs at various times, but probably helped more than hindered.
The Fiendish Heritage feat says you choose one of the alternative stat adjustments. So, when using the feat, you don't roll randomly, you actually pick and choose the one you want.
However, I don't think Fiendish Heritage is anywhere near worth a feat. I would allow one of those variant Tieflings without using it.
There's a middle way if you're not satisfied with it being a feat: make it a trait for your players to pick.
A third would be to change the feat to allow the player to pick the variant tiefling ability he wants, if you feel it's underpowered.
Personally I'm pretty happy with it as a feat, because it ensures that the player who wants to play a tiefling either wants to do so for the flavor and doesn't mind rolling randomly, or wants to have some control on his character and thus will choose to take the feat.
Alternatively, I'd probably agree that a player who rolls and gets three abilities he really dislikes should be allowed a fourth roll. But again, that's linked to your GMing philosophy - mine is to allow some minor things for my players that'll make them love and care about their character even more.