When does the pour matter? Especially when it comes to serving beer, such as Guinness, it is debatable that the pour is the most important aspect. This is something I understand due to the layering and carbonation...

When is it important to pay attention to the pour for other alcoholic beverages?

For example, I dated a waitress that was adamant about the proper way to pour wine - thumb in the bottom, on the forearm with a napkin, presenting the label during the pour, finally properly spinning the bottle at the end of the pour... Is this all due to presentation or does it have anything to do with consumption, as well?

Considering cocktails, I do not mean shaken vs stirred...
This is very broad so I will stick to wine in my answer. There are many considerations for pouring, you have the aesthetic aspects and presentation, and you have the mechanical aspects which can change the properties of the served drink. 

For wine, the waitress was right from a presentation point of view when served in a fine dining setting. Holding the bottle by the base gives the server the maximum reach with good control, twisting at the end helps reduce drips, the napkin can be used for any cleanup quickly, and showing the label assures the customer they are being served the wine of their choice. This technique does not effect the consumption, if you are entertaining at home there's no right or wrong way really, although I find the hold and twist give me the same advantages when I'm serving wine at my table. 

From a mechanical aspect, with wine the major considerations are sediment with red wines and bubbles with sparkling wine. If you have a red wine with sediment you need to be careful to not shake up the bottle and to leave the dregs in the bottom as you pour (or decant it through a strainer). With sparkling wine you need to be sure not to overfill. With most wines how you pour it makes no detectable difference on the flavor.