Given his so called popularity, James's appointment as headboy would have gone down pretty well with a lot of students except for most of the Slytherin students. As you may know, James wasn't exactly popular with a lot of Slytherin students (except Andromeda Tonks). Gryffindor and Slytherin have a 1000 year history of fierce rivalry and James Potter was often at the centre of it, whether it be through fierce clashes against Slytherin at Quidditch matches, or getting into arguments and fights with Slytherin students. There were even some nasty scenes when the two houses met on the Quidditch pitch during the 70s and 80s. If James Potter was appointed headboy, here is how I feel the Slytherin students would have reacted:
Slytherin 5th year prefect: "Professor Dumbledore has already got on with the job and has already appointed new prefects, a headboy, and a headgirl. On behalf of Hogwarts, we've got James Potter. He's the man who is going to assist the school and lead us prefects and the entire student body.
"If you were to think of the Gryffindor common room as a temple, well, Mr Potter is the high priest. A fanatic. In fact, there is only really one supremacist in this room and it's you [James] because you want red and gold flags, house anthems, house Quidditch coaches... you are a Gryffindor supremacist. "I frankly think that this appointment amounts to pretty much a declaration of war on our house (Slytherin)."
"I would argue what we really need is to have a sensible, common sense approach and for Dumbledore to recognise he has made a mistake and to find somebody who actually likes Slytherin to represent all of us."
This same 5th year Slytherin prefect later told her head of house Slughorn that Gryffindor Quidditch captain James Potter "dislikes" Slytherin and will be determined to give Slytherins a hard time. James did not appear to be at all ruffled by this Slytherin prefects speech and said a defiant response shortly after: "All the houses want to be governed and treated equally. Fair enough. It is our duty to make our roles as headboy and headgirl an advantage for everybody, no matter who they are or what house's they belong to."
A 7th year Slytherin prefect (someone in the same year as James) also made a similar complaint: "I cannot believe that Professor Dumbledore has selected Mr Potter as someone who will be leading and representing us prefects as well as the entire student body. I have been in this school for six and a half years and I have heard the ramblings of Mr Potter: I am telling you now, he is no friend of Slytherin.
The last time I spoke, I said that we need to be cool, we need to be calm, we need to ensure that we all get a balanced approach for all four houses. Mr Potter’s appointment is no good for the fairness of the points system, and no good for Slytherin Quidditch players who train hard for their. We all need the best balanced approach between the four houses as possible, and I ask you, please, to rethink Mr Potter's appointment and come up with a more neutral candidate."
Evan Rosier (7th year Slytherin) was pretty angry at this appointment: "James Potter hates everything we stand for which should mean a much harder time for us."
However, not all Slytherins were dissatisfied at James's appointment as this 6th year Slytherin shows: "Mr Potter, first of all, congratulations on your new appointment as headboy. I always enjoy listening to you because you're always determined and you're always consistent about what you believe in, and you described how there should be an equal number of people from all four houses in both the Order of the Phoenix and within the Auror department. Do you agree with me that there should be an equal proportion of people from all four houses in these two organizations and if I can assist in any way to achieve this, I've written a little in how it can be done quickly and I can give you a copy of one. Do you agree?"
James's response: "Well first of all, I have to thank the young lady for giving a positive assessment of my appointment, that's first time I've heard it from a Slytherin, and my answer to her is yes."
