Why did Mendeleev have problems arranging the elements #Te# and #I#?
Their atomic masses are the 'wrong way round'.
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.