Is a bent tetraheydral the only shape that doesn't have a precise angle (as in it's less than 109.5 degrees)?

I don't think so although I'm not exactly sure what you mean by a bent tetrahedral. Other shapes have different angles, of course; however, those are not exact either if there are unpaired electrons in some of the unfilled positions.

By the way, I think you meant

VSEPR, not VESPR

On one of my pages of notes, it lists all the different shapes and the bond angles that go along with them. Next to bent (2 lone pairs, 2 bonds), it says <109.5 degrees for bond angles. I don't understand why that one is less than 109.5, when a trigonal pyramidal isn't.

NH3 is less than 109.5.

NF3 is less than 109.5.
SO3^-2 is less than that.
H3O^+ is less than that.
SOCl2 is less than that.
In fact, as long as there is at least one lone pair, the angles will not be 109.5o
If you remove the lone pair, by for example, making NH4^+, then you get the 109.5 back.

But is a molecule with an electronic geometry of tetraheydral and a molecular geometry of bent the only one like that? Why doesn't a square pyramidal have <120 degree angles when it has a lone pair? Or does it? I feel like more of the bond angles should be less than the listed angle for 0 lone pairs per electronic geometry type, but it only says for the bent shape that it's <109.5

No, a bent tetrahedral is not the only shape that has an angle less than 109.5 degrees. In fact, there are several other molecular geometries that deviate from the ideal angle of 109.5 degrees due to different factors such as lone pairs of electrons or repulsion between atoms.

Here are a few examples:

1. Water (H2O): Water molecules have a bent shape with an angle of approximately 104.5 degrees. This happens because oxygen has two lone pairs of electrons that repel the bonding pairs, resulting in a compressed angle.

2. Ammonia (NH3): Ammonia molecules also have a bent shape with an angle of around 107 degrees. Nitrogen has one lone pair of electrons, causing a slight compression in the angle.

3. Sulfur dioxide (SO2): Sulfur dioxide has a bent shape with an angle of about 120 degrees. This occurs because sulfur has two lone pairs of electrons, which push the bonding pairs closer together.

These examples illustrate that molecular geometry can be influenced by different factors such as lone pairs, repulsion, and the nature of the bonding atoms, resulting in angles that deviate from the ideal tetrahedral angle.