There is one sort of artifact which is to do with preparation: for example, in electron microscopy the samples are freeze dried. So, you may see structures that are artifacts of the drying process and not present in the living cell.
An artifact is damage caused by a preparation technique and can easily be confused with the sample’s microstructure.
Sample Preparation Handbook for Transmission Electron Microscopy
In more theoretical sciences, artifacts are often part of the data processing process. A familiar one is the characteristic fringing you see on using JPEG compression.
A compression artifact (or artefact) is a noticeable distortion of media (including images, audio, and video) caused by the application of lossy compression
Compression artifact, Wikipedia
Sampling can also create artifacts, for example if you are taking data below the Nyquist frequency.
MRI artifacts are numerous and give an insight into the physics behind each sequence. Some artifacts affect the quality of the MRI exam while others do not affect the diagnostic quality but may be confused with pathology.
MRI artifacts, Radiopaedia
One of my favourites: the lost city of Atlantis (spoiler: it's not real).
