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Do different sequences of bits exhibit different characteristics when sent over a network.

For example, does one sequence of bits have a higher error rate than another sequence? If there are differences, are they true in theory and in practice?

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    To prevent that, bits are encoded into symbols that are sent over the medium. Different media and protocols use different encoding.
    – Ron Maupin
    May 25 '20 at 14:56
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I'm assuming you mean user or payload bits. The physical layer uses line codes and scrambling to prevent transmission problems for certain bit pattern.

Sometimes, this is less successful (early 100BASE-TX) but usually the encoding takes good care of that problem - so no, the user bit sequences don't (or shouldn't) matter.

However, in very special cases, specially crafted "killer packets" can cause too much DC energy to be generated for the PHY to handle, so the transmission breaks down.

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