A Chinese teacher once told me that you can only put two positive or two negative adjectives in this construction. Is this correct? So I couldn't say for example:
Many thanks! G
The "一方面。。。另一方面。。。" Structure can be used in the following ways:
1."On one hand...on the other hand (is also)..." (where the two adjectives are conflicting with each other.)
For example: 一方面貪心，另一方面(又)正派
On one hand he is greedy, on the other hand, he is (also) honest. (would he pick up the suspicious bag that has a dollar sign on it?)
*(又) can be omitted
2."On one hand... On the other hand (is also)..." (where the two adjectives are reinforcing each other.)
For example: 一方面貪心，另一方面(又)愚蠢
On one hand he is greedy, on the other hand, he is also foolish, (that's why he picked up the suspicious bag that has a dollar sign on it.)
*(又) can be omitted
So your teacher said you can only put two positive or two negative adjectives in this construction is partly right, it applies only when the two adjectives are reinforcing each other.
*Unrelated to your question about "two positive or two negative adjectives in this construction." The "一方面。。。另一方面。。。" structure can also be used in the following way:
"From one side...and from another side..." (when two events/elements are happening at the same time.)
For example: 一方面受外敵攻打，另一方面受內亂困擾
On one side, being attack by outside enemy, on other side suffering from internal upraising
As for your example sentence 我哥哥一方面有名，另一方面不帅。 "有名" and "不帅" are in conflict with each other when it come to attracting ladies, the sentence is understandable, but it does not fit well into a straight "一方面。。。另一方面。。。" Structure, It only work if antonymous conjunction (like: 但/但是、而、不過、可是) are added, like Farnz Seager suggested or rephrase it to 我哥哥虽然不帅，但很有名 as Gangosa suggested would be better.
The following sentence expresses admiration for and doubt of someone, which I think are respectively positive and negative.
On the one hand I admire his talent, but on the other hand I doubt his judgement.
"admire" and "doubt" are the contrasting items.
Your sentence is not good, because 一方面。。。另一方面 should contain opposites or contrasting thing.
Your sentence might be expressed like this:
Edit: Here are 2 sentences, neither of which contain, to my mind, opposites or contrasting things, both of which use 一方面。。。另一方面
They are driven on partly by a wish for democracy, but also by a desire for national self-assertion.
'democracy' and 'independence' are not mutually exclusive or contrasting things for a nation state I believe.
The British media have created a fierce controversy over Oxford's admission procedures (my note: which are elitist) and elitism in general.
'elitist admission procedures' and 'elitism' are not contrasting opposites.
Tang Ho, I hope you do not think 'talent' and 'judgement' are adjectives??
I repeat: Although, talent and judgement are not adjectives. (OP specifically mentioned 'adjectives' in his post.)