Question: Which way are arrows supposed to point on a tabbed web page? Towards the selection or towards the body of the selection? An awkward scenario seems to arise when a user selects another item and the arrow moves to point at nothing in particular when the arrow is pointing to the body. Is there a best practice? 

![enter image description here](https://i.stack.imgur.com/WgSMw.jpg)

Answer: 
Which relationship do you want to emphasize? Use that to inform your decision. The down arrow in your image indicates a relationship of "is title of" or "is detailed by" or even "has child", whereas the up arrow indicates a relationship of "is detail of" or "has title" or even "has parent". 

I suspect the down arrow is more common and thus familiar to more users. In CSS selectors, for example, the ">" operator is for the "has-child" relationship (points from parent to child). Is your user domain consumers? Then I would consider the down arrow. Only for IT or math domains/users have I frequently seen an arrow point from child/leaf back to parent/owner.

On the other hand, especially if your domain is new or unusual, you could remove the directional question with a nondirectional or bidirectional solution.

Spotify Help has a nondirectional highlight between the selection and body:
<https://support.spotify.com/us/>

![enter image description here](https://i.stack.imgur.com/JxhsS.png)

Essentially:

![mockup](https://i.stack.imgur.com/ieQfX.png)

[download bmml source](/plugins/mockups/download?image=http%3a%2f%2fi.stack.imgur.com%2fieQfX.png) – Wireframes created with [Balsamiq Mockups](http://www.balsamiq.com/products/mockups)
If you are going to use a skeuomorph you should avoid unnecessary and baroque decoration

Here's some originals from my current desktop (the wooden one) to help us understand what it is we are trying to represent to the user:

![enter image description here](https://i.stack.imgur.com/FX5aI.png)
![enter image description here](https://i.stack.imgur.com/q37VA.png)
![enter image description here](https://i.stack.imgur.com/DP8cC.png)

Arrows don't add anything to this visual metaphor, they only serve to distract and confuse.

As an example of this deleterious effect, I cite the confusion that motivated your question.