Please note: I am not writing this about any particular leining or baal keriah I have ever heard. That's not an empty disclaimer; it's serious.
People who listen to kriat haTorah [the public reading of the Torah in the synagogue] value different elements:
Some listen for ivra, the proper pronunciation and accenting of letters and words.
Others listen for accurate and pleasant musical renditions of the notes.
Some look for a pace and an enunciation that will allow them to hear each word clearly.
And still others listen for a pattern of emphasis that indicates an understanding of the words being read.
For me, the most important aesthetic [as opposed to halachic] element of leining is Passion.
I am disappointed when I hear "Cardboard Leining", when the words are pronounced and sung properly, according to halachah, but without heart. Torah should be exciting, emotional!
I want to hear a baal keriah who reads the words in a way that shows the emotion behind them – the anger, the joy, the fear, the humour of a particular passage.
This is not confined to the "story" parts of the chumash, either; many of the Torah's laws can also be read with emotion. Think, for example, of Shemot 28:29, "And Aharon will carry the names of the children of Israel upon his choshen hamishpat breastplate when he enters the sanctuary, as a memorial before Gd." Or Shemot 29:45-46, "And I will dwell among the Children of Israel, and I will be their Gd. And they will know that I am HaShem their Gd, who took them out of Egypt to dwell in midst; I am HaShem their Gd."
Perhaps if we had a more emotive leining, the Torah reading would be less of an opportunity for people to read articles or step outside.