Nearly all of the analogue thermometers are, or can become, inaccurate.
The ones I have can be twisted to re-adjust the position of the needle.
I used to calibrate them in a pot of boling water every now and then, but it was something that needed to be done every few weeks.
In the end, I worked to lose my reliance on them. I did a number of jugs of milk without the thermometers in them, getting used to judging the feel of the jug. I use my right hand to hold the jug handle and use my left had to check temp. In the early days, I would quickly put the thermometer in my milk at the end to see how close I was. You soon get pretty good at judging the right temperature, or at least getting close without burning!
Cant speak for the digital ones personally, but have heard from others that they are just as unreliable.