Our dm is treating our "1" damage rolls as a natural 1. So when you roll a 1d4 and you do 1 dmg (after succeeding hit dice) we get an especially bad outcome. Is this normal procedure?

No, this is not normal.

By the book, critical failures only (kind of) happen on death saving throws.

Even for DMs that use crit fails on attack rolls, they are usually only on the attack roll (the d20), not the damage roll (the d4 in your example).

Having a 25% chance of a crit fail on a dagger attack is completely ridiculous!

No it's not normal, and it's unfair to a lot of builds

Nothing in the rules calls for a critical fail on damage rolls, not even the DMG optional rule on critical failure.

Anything that rolls a lot of small dice for damage will be at a disadvantage. Beyond that, anything that isn't rolling as big a die as possible for damage is disadvantaged. This unfairness includes rogues, spells like Magic Missile, Fireball, or Cloud of Daggers, or basically anything other than a 2-handed weapon-focused character. A d4 damage die has 3 times as much chance to critically fail as a d12 using this rule.

What? No. Stop that.

A damage roll just gives you the numerical value for how many hit points a creature loses as result of a successful attack. There should be no narrative outcomes of this except things like, "they got a good scratch on the arm" or "they're limpy and coughing up blood now" to visualize how the creature's overall health is as a result of the attack. This is an incorrect use of the "critical failure" which is primarily designed as a worst-case-scenario on ability checks (when a character is doing something with risks and consequences).

It really shouldn't even apply to simple tasks that a character would normally excel at (you shouldn't crit, nor even roll dice, to put on your boots).

Critical failures are designed for when a character wants to sweet talk a guard into opening a protected door or swing from tree branch to tree branch like Tarzan. These actions have real consequences (both negative and positive) and so both a guaranteed success (20) and a guaranteed failure (1) are part of the game's chance systems. A d4 damage roll is not part of any chance system built into the game, other than how much damage is done (e.g. a little, some, or a lot)...plus, if a damage roll is taking place, the character has already succeeded in what they were trying to do! :)

Oh, and all that said...there is no mention of critical failures in Fifth Edition.

Critical hits yes, but as far as rules go, critical misses are not even mentioned in the Player's Handbook or the Dungeon Master's Guide. I assume you are playing with the "house rule" of using critical failures as your DM has gone to an extreme, but the point of order discussed by others here is definitely worth noting as there are no official rules in 5e for critical failures.

It's not normal. It also becomes increasingly more punishing at higher levels.

The litmus test I've learned to use is the Kung-Fu Kraken / Straw Dummy test. It was originally developed for Pathfinder, but is more broadly applicable than just that system. The following is taken from my reading of the post, and the quotes are directly from the post.

The actors we have in this example are:

1. The Kung Fu Kraken (or in 5e, the action surging 20th level fighter or the machine gun Sorlock)


2. Janet the Janitor, a first level commoner

The two tests that are described are:

1. Straw Dummy Test: If a character is fighting against an inanimate object for 10 minutes (100 rounds), how likely it is that they're injured? Without action surge / quicken spell, our KFK makes 4 attacks per round, for a total of 400 attacks. At a 10% rate of 1's (on a d10 for damage), they'll have rolled 1 about 40 times.

The point of the straw dummy test is to measure how severe the consequences are for a fumble, when someone hits something that can't fight back for an extended period: if the warrior, after 10 minutes, is bleeding, dying, missing a limb or generally looking like they've lost a fight, then there's something wrong from a verisimilitude standpoint, and the fumble rule has failed the Straw Dummy test.

2. Bad stuff should never happen to the Kung-Fu Kraken more often (on a per-round basis) than the Janitor. At 20th level, an action surging Fighter or a machine gun Sorlock makes 8 attacks. Janet makes a single attack per round. Janet, using a dagger, has a 25% chance of rolling a 1 on a given round. Using a d10 for the fighter / sorlock, they have a 1 - (0.9^8) = 57% chance of rolling a 1.

No

I'd possibly say a natural 1 on an Attack-roll might be a critical failure
(e.g. You went to go skewer your opponent and accidentally let go of your weapon, so now you're unarmed and your weapon needs to be retrieved or re-roll an attack against another nearby target [possibly friendly] or something of that ilk, where you're now disadvantaged). I figure if there's a 5% chance of doubling damage, there's an equal 5% chance of royally flubbing it, and just to make things 'interesting'.

However, Damage rolls are NEVER treated as failures (or critical failures). Of course, resistances and hardnesses could reduce damages to zero -- i.e. you hit the target, but, failed to cause damage.

I'm not sure how/why a 1 on a damage roll would be a critical failure...I'm just trying to see/justify a rational how certain weapons would have a huge chance of failure and if so, does rolling a natural max die roll increase damage??
Personally, I can't see ANY rationalization of this.

Nope, per RAW, a critical hit or critical fail can only occur on rolling a "20" or a "1" on the D20 specifically for attack rolls.

You cannot roll a critical hit or fail on a D4-D12.

This is a pretty bad rule, basically increases your chances significantly of rolling a critical failure, and also adds a crit fail possibility to spells that call for a saving throw.

Definitely talk to the DM, if this is just a misunderstanding than easy fix, if he insists on keeping the rule, might need to look at finding a new game.