If the Landsat images are available, it is better to first mosaic them and then classify. This way, you may avoid several sources of error. If this solution is not possible, look how the land cover attribute is assigned (that is, to the center or UL of the pixels ?).

Thank you very much for your answer. The area we ares studying is relaitvely big and ecologically diverse, therefore it is not possible to mosaic images first, we even had to split some images so that we get good clasificacion. What do you mean with UL of the pixels?

UL means Upper Left corner of a pixel. Most of the times, the pixels are referred as respect to their center or UL; other three corners may be used, depending on the program. In your particular case, this means 15 m difference both in x and y (or 30 m, if an image is referred either as respect to its upper left or lower right corner of their pixels). So, you have to verify in ArcGIS documentation how this software is referencing the pixels; if you are allowed to choose, you must select the same option (for example, center) for all your images. In addition, look current and upstream steps: (i) how exactly the mosaic is performed in ArcGIS ? (ii) how the images you have to mosaic have been generated, i.e., was ArcGIS, or other software - Erdas, Envi etc - used for all of them ? etc..

Seems that one pixel shifting during mosaic process, is related to lack of resamling to resolve pixel misalignment. There is an option in ArcGIS 10, you can adjust during mosaic process, called "mosaic_tolerance". It default value is 0.5, but you can set any value from 0 to 0.9999. Seems that adjusting of this parameters can help in this case, you can set low value (or even 0) of mosaic_tolerance to force program make resampling instead of one pixel shift when misalignment is detected.