How can hard drives store so much data and before it fails, be so reliable to give back all the bits without any error?

"Tons of reasons, many of which are far too complex for me to even understand. They're shielded from electromagnetic radiation (well, background levels anyway), and contained in a sealed, dust free container.

As for error handling:

Error handling

Modern drives also make extensive use
of Error Correcting Codes (ECCs),
particularly Reed–Solomon error
correction. These techniques store
extra bits for each block of data that
are determined by mathematical
formulas. The extra bits allow many
errors to be fixed. While these extra
bits take up space on the hard drive,
they allow higher recording densities
to be employed, resulting in much
larger storage capacity for user data.
[14] In 2009, in the newest drives,
low-density parity-check codes (LDPC)
are supplanting Reed-Solomon. LDPC
codes enable performance close to the
Shannon Limit and thus allow for the
highest storage density available.
[15]

Typical hard drives attempt to ""remap""
the data in a physical sector that is
going bad to a spare physical
sector—hopefully while the number of
errors in that bad sector is still
small enough that the ECC can
completely recover the data without
loss. The S.M.A.R.T. system counts the
total number of errors in the entire
hard drive fixed by ECC, and the total
number of remappings, in an attempt to
predict hard drive failure.

From here.

The rigidity of the innards and the fact it's a sealed, solid unit means small vibrations shouldn't create a bad write, though it can happen to potentially quite disastrous results. It uses the air pressure inside the sealed container to keep things running smoothly. Things go wrong quite often, even with ECC, which is partly the reason for hard disk recovery tools, redundancy and the like."

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