If a qubit can be a 1 or 0, and will return both - how can we rely on it? In essence, a qubit may 'present itself' (upon observation) as a 1 or a 0. My understanding (as inaccurate as it may be) is that the observation of one particular qubit may result in different outputs. It may be 1 upon first observation, and 0 the next.
That said, how does this help us when we wish to know (definitively) whether it is a 1 or a 0.
If I ask someone a question, and I can not rely on what they say - I don't have a reliable answer. How is this different? At least with a 'traditional' bit I definitely have a 1 or a 0.
So, I assume (again, possibly wrongly) that this qubit's output must be interrogated a little further and calculations done to ensure the integrity of what it outputs in order to find the most probably output (i.e. a 1 or a 0). In which case, if it is either a 1 or a 0 ultimately, it doesn't store multiple values at once. Which means it's no more efficient than a bit which, similarly, stores only one value at once.
Let me be clear - I'm misunderstanding something here, I'm fully aware of that, I am definitely wrong - but I want to know what part of this story I'm missing.
Question/s
If one single qubit stores one single value (however we extract that value) - how is it any more capable than a classic bit? If I'm misunderstanding, and in fact a qubit can store multiple values and will output either - how can we persist and retrieve data that way?
 A: A single qubit is about as useful as a single classical bit in a normal computer. You can only really do three things to a classical bit:

*

*Write a value to it, like 1.

*Read that value, still 1.

*Flip it, now it's a 0 (woo! computation!)

The power of a computer comes from using many bits, which allows the storage of diverse kinds of data once someone figures out how to encode data (text, numbers, images, sounds, etc.) in bits. It also allows more sophisticated manipulations of the data since changes in one set of bits can depend on the state of other bits.
Similarly, there's three things you can do with a single qubit:

*

*Write an amplitude to it: $a\left|0\right> + b\left|1\right>$ where $a$ and $b$ are complex numbers and $|a|^2 + |b|^2 = 1$. $\left|0\right>$ and $\left|1\right>$ are labels for the simplest states of a qubit.

*Read it: get 0 with probability $|a|^2$ and 1 with probability $|b|^2$ (hence the sum equaling 1 in step 1.).

*Rotate it: transform the numbers $a$ and $b$ into new values while still satisfying step 1.

Here's a better explanation of this setup with puppies by CalTech physicist Sean Carroll.
The Saturday Morning Breakfast Cereal comic linked to by Emilio in the question comments is a great layman's description of what happens (as it should be; it was co-written by Scott Aaronson, a computer scientist at the University of Texas at Austin who specializes in quantum computers). Once you have your computational problem encoded in qubits, there is an operation you can do with qubits that has no counterpart in classical bit computing: interference. This operation takes a set of qubits representing possible solutions to a problem and, with proper encoding, causes the possibilities corresponding to wrong answers to cancel out, resulting in a near-zero amplitude, leaving only the right answers to be detected. To put it another way, a properly set up quantum computation causes wrong answers to destructively interfere and correct answers to constructively interfere.
The result is still probabilistic, so it's still possible to get a wrong answer. But, a carefully designed quantum computer can have a 99.99..% chance of returning the right answer. Running the computation multiple times and taking the majority answer can make the probability of a wrong answer arbitrarily small.
Quantum computers don't get their speed from "trying every possibility in parallel." It still takes processing to encode the problem and solution space into the qubits and perform the necessary transformations. In fact, based on our current knowledge of quantum computers, there are only a handful of problems that quantum computers solve significantly faster than classical computers--Shor's algorithm for factoring numbers being the most famous--and each problem requires a unique setup. As far as we know, there are no universal quantum computers that can solve all problem faster than a normal computer.
To answer your specific question, qubits are only meant for processing data with special algorithms. Think of it as a special kind of RAM, not a hard drive. Storing data is best done with classical bits.
