Is sequencing error a function of the nucleotide being read?
Unfortunately, it does depend on sequencing techniques.

For example, in Illumina sequencing, each sequence fragment is amplified (in order to get a stronger signal) and forms a cluster on the microarray. Each cluster is sequenced by cycles of:


Adding fluorescent terminator nucleotides. These nucleotides are modified to contain an inhibiting/terminating group and prevents more nucleotides from being added. Theoretically, only one nucleotide is incorporated into every DNA fragment in this step.
Washing off excess nucleotides.
Capturing the incorporated nucleotide using imaging techniques and determining which base was incorporated (based on the colour of fluorescence).
Cleaving the terminator from the added nucleotides, so that the reaction can continue. 




Image from Metzker, 2010.

This way, each fragment is synthesized, one nucleotide at a time, and each nucleotide that is incorporated gets detected. However, the first step is not flawless: sometimes more than one nucleotide gets incorporated into a certain DNA fragment, or no nucleotides get incorporated. Eventually, the DNA fragments in a cluster (all containing the same sequence) will fall out of sync ("phasing") and the fluorescent signal will become less clear, with a mixture of different colours. This is the main cause of sequencing error for Illumina machines, and also the reason why Illumina reads are relatively short (~300bp).

So to answer your question, in this example, nucleotides may be erroneously read as nearby nucleotides in that sequence. Errors will vary using other sequencing methods and how those methods work.

The article I linked earlier explains various sequencing methods in more detail. (Unfortunately, it's behind a paywall so some may not be able to view it.)