Preferably a word that is not specific to the mess being one of disorganization. Someone who spills things, for example, should be included.
I would call them a klutz:
a person who often drops things, falls down, etc. : a clumsy person
A slob. That's not to do with disorganisation, it's more like someone who doesn't clean up around their house. Oxford Learner's Dictionary defines slob as "a person who is lazy or rude or who dresses carelessly". I'd add "generally untidy and messy in habits," and is the word I would use in your case.
awkward and clumsy are nonspecific terms and may fit, but if you mean awkward and clumsy with one's hands, "all thumbs" is a better choice.
- "Can you thread this needle for me? I'm all thumbs."
- "Her clumsy hands are likely to drop the cake on the floor."
- "He was so awkward and hasty that he kicked my poor puppy."
It's informal and a Yiddish loan word, but nothing fits the bill better than "schlemiel". The OED regards it as North American and informal and gives as its meaning, "a stupid, awkward, or unlucky person". Vocabulary.com indicates that the word derives from "Peter Schlemiel", a bungling character in a German fable. The aspect of being unlucky is better expressed by the perhaps less common "schlimazel" (literally, bad luck). This is expressed by the aphorism: "A schlemiel is one who always spills his soup, schlimazel is the one on whom it always lands."
Informally, I would call that person Butter Fingers.
noun. A person who drops things inadvertently or fails to catch things; clumsy person.
Just an info: In EA Sports Cricket '02, there is a cheat code which would make the fielder drop the catch every time and for that you need to enter Butter fingers. Clumsy fielder.
Similar to klutz there is also lummox - a clumsy, stupid person [oxforddictionaries.com]. To me the word implies a kind of clumsy dull-wittedness that comes from being sleepy, hot and bothered or drunk; not necessarily someone who is permanently stupid.
I'd also like to suggest a couple of euphemistic ones:
hooligan - could be someone who makes a mess through aggressive, careless, or destructive play, or some wild abandon. "will you hooligans stop playing football in the house, you're making a terrible mess" or "stop stirring the paint like a hooligan, it's going everywhere".
whirling dervish - Dervishes are a Muslim religious order noted for their wild, ecstatic dancing and whirling. This could be used to describe someone who rapidly and noisily leaves a trail of destruction/mess in their wake - "you burst in here like a whirling dervish upsetting everything as you go, please just sit down".
I'm a very messy person.
You could use a metaphor that conjures imagery of messiness. For example a storm.
For example - sometime's I'm referred to as Tornado Dave.
You could say that they are sloppy: (from Merriam Webster)
not careful or neat : showing a lack of care, attention, or effort
This is particularly appropriate to the case of someone who carelessly spills things on them since it carries the connotation of wetness (eg. mud/"sloppy joe" burgers (which spill their contents on you as you eat them): (Etymology from Etymonline)
1727, "muddy," from slop (n.1) + -y (2). Meaning "loose, ill-fitting, slovenly" is first recorded 1825, influenced by slop (n.2). Related: Sloppily; sloppiness. Sloppy Joe was originally "loose-fitting sweater worn by girls" (1942); as a name for a kind of spiced hamburger, it is attested from 1961.