Yes, there is a inherently inaccuracy caused by the delay between a position is determined by the GPS receiver and the time it is transmitted.
However, for installation certified for the EU and USA ADS-B regulations, the inaccuracy is very limited. The accuracy of ADS-B is therefor better than radar even when ignoring the latency in radar systems.
The first part of the latency is caused in the GPS unit itself; there is some processing time between the position signals arrive at the GPS antenna and the of the time of output of the computed position. Further delay can occur if the GPS-receiver is not directly wired to the transponder. If the position signal has to travel through another box (for example the ADIRU) additional latency can occur.
Finally the position arrives in the transponder and is delayed until the next position message is scheduled for transmission.
In installations certified for the ADS-B mandates of the EU and the USA, the position latency is limited to 0.6 seconds. This is usually achieved by direct wiring the GPS to the transponder. Additionally the latency is compensated for by extrapolating the position using the ground speed vector. The position within the transponder is thus update periodically (e.g. at 10 Hz) using the groundspeed vector. This extrapolation reduces the effect of latency by introducing a small error based on the accuracy of the groundspeed vector and any manoeuvring going on.
The total accuracy of the ADS-B signal is the combination of
- GPS accuracy
- accuracy of speed vector used in the latency compensation
- manoeuvring going on between the time of position validity and time of transmission not compensated for by the linear extrapolation using the speed vector
- residual uncompensated latency
In some installations the residual uncompensated latency is negative (i.e. the position is over-extrapolated). The limit is 0.2 seconds ahead of the current position. The recommendation in the ADS-B Minimum Operational Performance Standard (MOPS) is that the uncompensated latency should not be more than 0.4 seconds.
Note that most of the inaccuracy due to latency is only observable in the along-track direction.
The magnitude of the position error caused by the latency is very limited.
For an aircraft flying 270 meter per second (972 km/h, 525 KTAS), the upper bound of 0.6 seconds latency limits the error to 162 meter. That is much better than the position accuracy that en-route radars typically achieve (and in addition, radar also has latency).
In the TMA, the speeds are usually slower and so are the latency induced errors. So ADS-B here outperforms the TMA radars.
For reference, the 0.6 seconds is a limitation in the USA is from FAA AC20-165A (PDF) and in the EU from EU 1207/2011 (applicability dates amended by EU 1028/2014). The full Certification Specifications for ADS-B in the European Union can be found in the CS-ACNS.