What evidence can we find to show that Willy misses the distinction between being loved and being well liked?
The evidence that we find that can show how Willy misses the distinction between being loved and being well-liked includes the fact that Willy, in a commonly-seen ego-trip, elects to have a mistress whom he treats even between than his wife. This mistress is perhaps a woman that he meets during one of his many business trips back in the time when he would decidedly conclude that being well-liked is the secret to success.
A man with a mentality of this sort will likely engage in a superficial and physical relationship with no real depth because it would satisfy his immediate need for attention. Additionally, treating this outsider woman with gifts that are expensive, namely stockings, places Willy in a situation where he is in complete control, or so he thinks.
We know that behaviors like this are initiated by persons who prefer being adored, admired, liked, or lionized rather than being loved and protected. The latter is too boring and prudish for a person like Willy. Hence, he is willing to risk his marriage and family, not to mention the individual lives of his two boys and his wife, for the sake of one moment of complete hedonism.