Strictly speaking, Critical Failures don't exist in 5E

There are three kinds of d20 rolls: attack rolls, ability checks, and saving throws. However, ability checks and saving throws do not automatically fail on a natural 1. The times when natural 1's have a significant effect are called out explicitly for some rolls, but not for all rolls in general.

Nat 1's auto-fail for attack rolls

Rolling a 1 or 20, PHB pg 194

[...] If the d20 roll for an attack is a 1, the attack misses regardless of any modifiers or the target's AC.

Nat 1's have a crit fail-like effect on death saves

Meanwhile, death saving throws are a special case of saving throw in which it is possible to fail in a much more severe way when you roll a 1, as opposed to another low roll that would simply fail it.

Death Saving Throws, PHB pg 197

Rolling 1 or 20. When you make a death saving throw and roll a 1 on the d20, it counts as two failures. [...]

Conclusion

The PHB never says "critical failure" for anything, but it explicitly calls out effects that happen on natural 1's for attack rolls and death saves. Meanwhile, ability checks and general saving throws do not get this same treatment. This means they do not auto-fail or crit-fail on natural 1's.

Variant Rule in the DMG

The DMG calls out that you may implement critical failure or success on ability checks or saving throws. This reinforces that critical fails or successes do not exist out of the box, but you are given text in RAW to support their implementation.

Critical Success or Failure, DMG pg 242

Rolling a 20 or a 1 on an ability check or a saving throw doesn't normally have any special effect. However, you can choose to take such an exceptional roll into account when adjudicating the outcome. It's up to you to determine how this manifests in the game. An easy approach is to increase the impact of the success or failure. [...]

A potion of growth or an enlargement spell

By changing to medium size, temporarily, that disadvantage will go away. Both the potion and the spell make that possible.

Comment: this point got some discussion early in this edition's release. (This question is related but not identical, as is this one). This little piece of verisimilitude -- which parallels a similar rule about weapons for Large and Huge creatures not getting a damage increase if a medium sized creature uses it (DMG p. 278)-- avoids the absurdity of a halfling wielding a greatsword, while still allowing for a variety of other absurdities.

FWIW, this small sized character can ride a medium sized creature. Gnome and halfling Rangers (for example) can take good advantage of that if they are Beast Masters.

In the interest of Rules as Fun (RAF¹)

In making a ruling that is not strictly RAW, consider what is behind the character build, and the use it is making use of Small size. As the DM, consider the impact of ruling that the character counts as Medium for all rules purposes, such that the bulky paladin armor makes up the difference. In that case, a maul-wielding halfling might provide a bit of light comedy, but it would have very little impact on game balance. It's only if the player expected to get all of the benefits of Small and yet avoid any negative consequences of that size that the character concept begins to border on "cheesy" as well as funny. (Thanks to @NeilSlater for this point)

¹RAF

Regardless of what’s on the page or what the designers intended, D&D is meant to be fun, and the DM is the ringmaster at each game table. The best DMs shape the game on the fly to bring the most delight to his or her players. Such DMs aim for RAF, “rules as fun.” We expect DMs to depart from the rules when running a particular campaign or when seeking the greatest happiness for a certain group of players. Sometimes my rules answers will include advice on achieving the RAF interpretation of a rule for your group. I recommend a healthy mix of RAW, RAI, and RAF! (Jeremy Crawford, Sage Advice Compendium, page 1-2)