Why did Mendeleev have problems arranging the elements #Te# and #I#?

If you look at Iodine and Tellurium on the modern periodic table, you will find their atomic number increases (Te is 52, I is 53) but their atomic mass decreases (Te is 128, I is 127).

Mendeleev only had access to the atomic masses at the time he was developing the periodic table. Almost all other elements (there's another exception between Argon & Potassium, but he didn't know about the noble gases at the time) increase in atomic mass as you go down the periodic table, so other things did not pose this problem to him.

To put Te and I in the correct sequence Mendeleev looked at their properties.

Due to the fact that the properties of Te (tellurium) and I (iodine) did not match the patterns of the periodic table at the time, Mendeleev struggled to arrange the elements Te and I because, when the atomic masses were switched, the properties seemed to make more sense.