Let's agree for now that awakened toads and similarly weak creatures are a problem, and let's get back to the awakened cat for a moment. Would the awakened cat be balanced as a +0 LA creature?
Let's do a comparison with a *kobold* rogue rather than a human. This has two benefits: (1) most people agree that kobolds are on the low side of +0 LA, so this may provide a better test of whether the awakened cat is "barely +0 LA", and (2) the kobold actually shares some of the features of the cat (increased speed for it's size, low Str but high Dex, etc), which simplifies the comparison.
awakened cat Rogue 1
HD: 2d8+1d6 = 13 hp
Init +2
AC 14 (+2 size, +2 Dex)
BAB +1
Full (sneak) Attack: 2 claws +5 melee (1d2–4 + 1d6) and bite +0 melee (1d3–4 + 1d6)
Saves: Fort +3, Ref +7, Will +1
Abilities: Str 2, Dex 14, Con 10, Int 10, Wis 12, Cha 8
Skills: Balance +12, Climb +7, Hide +14, Jump +17, Listen +6, Move Silently +7, Spot +5, Tumble +10
Feats: Alertness, Weapon Finesse
kobold Rogue 3
HD: 3d6-3 = 7 hp
Init +1
AC 13+ (+1 size, +1 Dex, +1 natural, +armor)
BAB +2
Full (sneak) Attack: rapier +4 melee (1d4-2 + 2d6)
Saves: Fort +0, Ref +4, Will +1
Abilities: Str 6, Dex 12, Con 8, Int 10, Wis 10, Cha 10
Skills: Balance +9, Climb +4, Hide +9, Jump +4, Listen +8, Move Silently +7, Spot +8, Tumble +9, Craft (trapmaking) +2, Profession (miner) +2, Search +2
Feats: Alertness, Weapon Finesse
Note that I gave the cat max ranks in Tumble plus 5 ranks in Jump for the Tumble synergy, so it can try to avoid AoO's when entering an opponent's space to attack (DC 25). For their 3HD feat, I gave the cat Alertness and the kobold Weapon Finesse, so they're even there (both good feat choices for these characters, and they further simplify the comparison).
Combat-wise, the two may be reasonably balanced. Cat has more hp, more attacks, better saves, and (surprisingly) better skills. However, it has a 75% chance of attracting an AoO every time it closes with an opponent. Kobold has the chance to wear better armor, does *much* more damage per attack (7 pts sneak attack, versus something like 1-2 points per attack for the cat), and has more flexibility in weapons (I gave him a Finessed Small rapier here).
The fact that the awakened cat comes out with better skills is surprising, considering the fact that the kobold rogue gets 48 skill points and the cat only 14! The cat does get 28 points in racial bonuses, and can use Dex for Climb and Jump. The kobold obviously has more flexibility in which skills to focus on, but the cat can get higher total skill checks because their racial bonuses can be added on top of max ranks etc. For example, the kobold could have a +7 in Open Lock and Sleight of Hand instead, but the cat will always have a much better Jump and Balance check.
Overall, I'm willing to be generous and say that the awakened cat could be a marginal +0 LA, when compared to the (already underpowered) +0 LA kobold. The awakened cat rogue would fill a very narrow niche role, but for that role it doesn't seem to do significantly worse than a kobold rogue.
What do you think?