“ts” file are transport stream files. They are notoriously difficult for the editing engine to seek accurately. Shotcut is probably estimating the duration and having trouble matching up the audio and video. When Shotcut doesn’t come up with an image, it shows the checkerboard.
As an experiment, select a clip, and use the Convert to Edit-friendly Dialog to convert the file. Go ahead an choose the “good” quality level. See if you get better results with a converted file.