The network level is usually pretty solid in that regard with checksumming at wifi/Ethernet protocol level and at tcp, but that's the end of it for most systems.
TCP checksums are very basic. Ethernet has a proper CRC, which at least has certain mathematical guarantees about what it can detect. The TCP checksum fails if the same bit is flipped from 0 to 1 and 1 to 0 in the same bit position modulo 16.
modulo 16 really? I thought it is modulo 2^16-1 (size of multiplicative group of GF(2^16)) which is much bigger than typical packet size
The TCP checksum is based on the sum of all odd bytes and the sum of all even bytes. Adding a power of 2 to an odd byte and subtracting the same power from another odd byte will cancel out. I'm not sure what guarantees CRC-32 gives you, but they're better than that.