Absolute accuracy is not essential. What is essential is consistency. I am reasonably lucky to have a mercury thermometer which when bought was guaranteed to be accurate to within .25 of a degree. I also have a Kodak digital thermometer which didn't come with any guarantee of accuracy but when compared with the mercury one they read the same. I use the digital one in preference because it has a metal probe and responds to changes quicker than the glass mercury. It is also easier to use as well.
What I am trying to say here is buy a good thermometer and compare it with a certified one and note any difference. On the other hand there are so many variables that I don't think +/- 1 degree makes a terrific load of difference so long as you have consistency.