[Xenonman]

We had a practice about using huge TLC plates to separate acetyl salicylic acid and salicylic acid.

Which is the most polar one? Both are not-so-polar, but I'd say the ASA is somewhat less, because the -OH group has a clear, unprotected δ+ on the hydrogen, while the methyl in the OAc group distributes the deficiency in the three hydrogens and the carbon. The δ+ in the carbonyl is somewhat obstructed by the methyl and the rest of the molecule.

That's all I could think of. Am I wrong, right for the wrong reasons, right, or something else?
Links to the structures, because wikipedia
Salicylic:

ASA:

[discodermolide]

Both are very very polar molecules, can you say why? This is the main reason. Correct in thinking that ASA is less polar.
Shielding of charge by bulky groups does not contribute to the molecules polarity, which is basically your argument.

[Xenonman]

Reasons both are polar molecules:
- The aromatic ring subtracts density from the protons.
- The carboxyl group has δ+ on the C and H, δ- on both oxygens.

On second thought, the hydroxyl's proton is less electronegative and quite small, so the δ+ is somewhat more concentrated. The lower ΔEN of the C-O bondings makes the δ± lesser, which is distributed in the bigger radius of the methyl (which also distributes the deficiency in the hydrogens) and the carbonyl's carbon, which has a much bigger radius than the lone proton.

Similar to the difference between Cs⁺ and Li⁺, same charge in a much different volume mean a different charge density.

Is that it? 

[discodermolide]

You have 2 carboxylic acids here. They are the contributing factors to the polarity of these molecules.In solution they are in equlibrium with their corresponding anions. That is why these molecules are so polar. The next factor contributing is the phenolic OH making SA more polar than ASA.
It is about interaction with the solid material in the chromatography which I assume is silica.

[Xenonman]

Silica, certainly. And a mixture of solvents I forgot   
Does the phenolic OH cause an induction effect?  Ka_SA>Ka_ASA, so it makes sense.

Is there anything right in the third post?