What would be the the disadvantages if we had a popular vote instead of an Electoral College?

The main disadvantage here would be that the states would
come to matter less in our political system.  This would be particularly true of the
little states that do not have all that many voters in
them.

In the Electoral College, the small states are
overrepresnted.  This is because they have the same number of Senators as the large
states (and the number of votes a state gets is equal to the number of members they have
in Congress).  Because of this, there is some advantage to be gained by campaigning in
small states -- you can get more electoral votes there than those states are really
"worth" in terms of numbers of people.

The idea is that if
there were no Electoral College, candidates would ignore these small states and spend
all their time in the big states where all the people
are.

As the link that I have included
says

We would
probably see elections dominated by the most populous regions of the country or by
several large metropolitan areas.