I've had similar issues with ADS1118, especially when used at 5V. At 3.3V it was happening much rare, or not at all.
They are transmission error. To be more precise, my conclusion was those were reflections in the wires, wires that act like transmission lines with unmatched impedances at their ends. My guess was at 5V the chip was even faster, so any reflections were even more perturbing.
Ideally the impedance between the transmitter, the wire and the receiver should be adapted so they match, but in practice that might be not possible (at any impedance mismatch a signal is reflected back to where it came from, with the same or opposite sign - depending of the two impedances ratio - therefore after one or many reflections the voltage waveform of a signal is altered enough that the receiver sees a different bit than it was transmitted <- if this doesn't make any sense, read about reflections in a transmission line).
As a workaround, try adding some 10...1000 ohm resistors in series with the digital wires (at the transmitting side of each wire), and see if the communication improves. Shorter wires might help, too.