Keep adding fresh thinned ink during the press run. Ink gets thicker as you print. Try and maintain a steady pace as you print. Unnecessary delays in pulling the next stroke will result in drying in with solvent or waterbase inks. This is especially important when starting a run.
Many printers make the mistake of stopping and admiring the first print.
Ensure you have plenty of print-off paper, and instead of trying to assess all the variables that effect print quality, do them one at a time while maintaining the printing pace. Ensure everything is printing, adjust squeegee pressure, ink viscosity, and clean any clogs in the stencil. Check the color and adjust as necessary. Check the register and adjust, locking in tabs and frame before proceeding with the run. Pull a good print when all the above is good, and check at various times during the run against this piece to ensure nothing is changing.