I have burned many DVDs doing the time I was working with optical media (CDs & DVDs), but I have since moved on to using hard disks and USB memory sticks for most things. I only burn DVD's when it is not possible for people to avoid using DVD players, and I think I have developed a hate-relationship towards dedicated players, due to their poor support for burned media.
The compatibility problems I have had with DVDs has annoyed me, to such a degree, that I refuse burning DVDs for certain people, since there is a risk they will come back, blaming me if their broken DVD player, for whatever reason, will not play the DVD. Usually they will argue: "it is working with commercial DVDs".
The problem is with commercial players, that the format of burned disks is very poorly supported, and it will often lag and stutter, or even flat out not read the DVDs. On top of this, we also have different DVD media standards, there is +r and -r, and neither of them seems to work equally well in all DVD players. This is while commercial disks will usually play just fine in most players.
The reason for this situation is, most commercial disks are not burned, but rather pressed from a Glass Master. The process is also known as replication. So this is why you can play almost all commercial disks, given that they have the right region code (which is another reason not to buy DVD players).
Improving compatibility with players
Without knowing which kind of player the media is going to be played on, this can actually be hard. There is no "one-size-fits-all" solution to the problem. You should ask the company or read the manuel for the player that you are targeting. It is unfortunate, but there is no guarantee that your burned DVDs or blue ray discs will work on all players, not even if the player claims support for your burned discs.
Rest assured, however, that you most likely have done nothing wrong. The problem is with the player. This is not rocket science after all. Having that said, here is what you can do to greatly improve compatibility with DVD players.
1. Some players prefer -r discs, and others work better with +r discs. The +r format is newer, and therefor likely also more widely supported on newer players. So try to use +r disc first, and then -r if that causes problems.
2. Avoid rw discs as they are usually unnecessary, and have even more compatibility issues. When will you actually re-use a DVD anyway?
3. Try using CDBurnerXP instead of any non-free software, and avoid the build-in burn features in Windows, Media Player.
4. Try burning at a slower setting as errors occur more frequently at higher speeds. This could especially be important for older DVD burners. But generally, if the disks are approved to burn at x16, then you would also expect them to work at those speeds.
5. Test if the DVD is working on a computer. If you have used either -r or +r disk and not an rw disc, and the computer plays the disc, then the problem is with the DVD player.
What should I use instead of DVD players?
I recommend getting a HDMI or VGA cable, depending on what your TV supports, and then connect your PC or laptop to your TV. It may be inconvenient to connect your main PC, so you may want to get a dedicated PC for just watching movies and listening to music.
There really is no reason to buy a DVD or blue ray player. By using a PC you can also avoid problems with regional coding found on some commercial DVDs. Plus, you can watch Netflix or Google Play without having to get a dedicated device.