Typically within a few kilometres for fresh data — plenty for finding a satellite in the sky — but accuracy falls as the orbital data gets older.
The honest answer has three parts: how good the orbital data is, how old it is, and what you want to use it for.
The model this site uses, SGP4, is described by its maintainers as generally accurate at the kilometre level. That figure is for the model working on good, recent data. The errors are not spread evenly in all directions; they are largest along the orbit, so the satellite tends to be a little early or late on its track rather than off to one side.
Each satellite page has an Orbital Data Source row and an Orbital Data Fetched row. If the source says the data is cached or sample data, treat the position as rougher.
The simplest real-world test is a bright ISS pass. If the site says the ISS will appear in the south-west at 7:12 pm and climb to 60°, you should see it there within a minute or so of that time. If the station has just raised its orbit, the first passes after the burn may be off until new data arrives.
Check the Orbital Data Source and Orbital Data Fetched rows to see how recent the TLE behind the estimated position is. Open Cartosat-3
Two kinds of numbers on this site have different accuracy needs.
Positions on the globe. These need only to be right to a few kilometres; at globe scale that is far smaller than a pixel.
Pass times and directions. Here the useful measure is angle and time. A satellite at range ρ with along-track error Δs appears displaced by about Δs/ρ radians and runs Δs/v seconds early or late. For the ISS (v ≈ 7.66 km/s) seen at a range of 800 km, Δs = 3 km gives 3/800 rad ≈ 0.21° in the sky and 3/7.66 ≈ 0.4 s in time — both invisible to the eye.
The pass search itself adds almost no error. The code steps through the next 24 hours every 30 seconds, and when a pass starts or ends between two steps it bisects that interval until the boundary is known to within one second. The comment in the source says it plainly: a pass edge is not sharper than the model.
The larger risk is age. SGP4's secular drag terms grow with time since epoch, and errors in the fitted BSTAR grow with them. If a TLE is a week old, a low satellite can be noticeably early or late. That is why this site refetches data rather than relying on the seed TLEs baked into its code, and labels each data source on the satellite page.
Most uncertainty comes from drag, which changes how fast the satellite moves around its orbit; that makes it early or late on its track rather than shifting its path sideways.
They become wrong, because the old TLE describes the old orbit. Predictions improve once a new TLE is published after the burn.