Dalton's symbols are a small set of symbols used to represent the elements, and they had some interesting looks! However, Dalton also had some problems with his tables, arrangement , and symbols!
To start, his tables, such as those including relative atomic mass, do not have much basis in scientific fact (for example, zinc and copper are both 56 relative units of mass). He also has some diagrams of molecules, of which some certainly are correct! However, they are not represented in a way that really shows how the molecule is oriented geometrically. For example, his table in the link below does not show "bent" conformations for some 3-atom molecules, which is to be expected considering VSEPR would not be developed for some time!
Dalton's symbols also did not have the systematic method of organization that we have today with the periodic table. We have elements arranged by number of protons and (de facto, not by design) by atomic mass. So, it would be difficult to add in the new elements we've discovered systematically, and it would be difficult to find symbols for these new elements.
Dalton's symbols, finally, did not have much of a system for their creation. The chemical symbols we have today are simply abbreviations of names. Dalton's symbols were drawings that do not offer much ability to expand the list of elements as necessary!
This is not all to say that he was not a brilliant chemist! He did some major pioneering of the field, and his atomic theory holds pretty well for most normal situations in chemistry! In fact, the atomic mass unit is named for him. Now, we often don't see this in chemistry, but in biochemistry and biology you hear about proteins' weights in Daltons all the time!
I hope that makes sense!