When preparing a video file to be submitted for broadcast TV (NTSC HD), should I preview it on a TV to make sure there is no interlaced related issue?

IOW, could any problem show up only on TV (interlaced display) but not on a computer monitor?

And if I do need to preview it on an interlaced display, can I just set my video card refresh rate to 60 hz interlaced, and then play the video on the computer? Or do I have to burn a DVD and play it on a real TV?

The simplest answer is when HD digital broadcasting started they adopted 1080i standard and still use it today, despite the fact that most people use flat screen tvs. Interlaced was first introduced as a clever way to overcome the limitations of early broadcast tv. In essence, interlace reduces the bandwidth needed in half which is still useful.You could look up its history to get a better understanding but for your purposes it's probably not necessary.

If you plan to provide content for broadcasting, let's say for a local tv station, it would be best to ask them what they will accept. Otherwise most videographers today prefer to film and produce progressive because it looks better but it can always be converted to interlace if need be.

There are many wrong ways to introduce the necessary pull down to progressive footage before final delivery in 60i. I find it worthwhile to preview the final deliverable on an actual television using an appropriate device. I’ve used 60i ProRes playing back on an Atomos recorder via HDMI to a TV before, as well as a variety of video I/O devices like the Blackmagic Mini Monitor straight from computer to television. If you’re doing a 23.98p to 60i type of conversion, everything is going to look terrible on a regular computer monitor.