How do traits with no negative effects get "weeded out" via evolution?
Oops I wrote a lot! This is almost a very brief introduction to some concepts of population genetics.

A little bit of terminology first

Locus

A locus (plur. loci) is a position on a chromosome.

Allele

At a specific locus, different individuals may have different variants. One individual might be ATTCTA while another might be ATTCAA for example. These variants are called "allele". The whole goal of evolutionary genetics is to understand the creation (mutation) and change in frequency of the different alleles in the population.

Heterozygosity

You probably know that in many species, we carry two copies of each chromosome. One individual can therefore carry twice the same allele at a given locus or can carry different alleles. Expected heterozygosity ($H$) at a given locus is the fraction of the population that carries two different alleles at this single locus.

Fixation

When an allele reaches a freuqency of 1 (100%), that is only this allele exists in the population (and therefore the other alleles have been wiped out), we say that it has reach fixation.

Natural Selection

The process you describe in your first paragraph is called natural selection.

Natural selection is a fitness (=a function of both reproductive success and survival) difference between different genotypes. As you said (but with other words), deleterious alleles will decrease in frequency through time and will eventually end up being weeded out from the population through natural selection.

Genetic Drift

There are other evolutionary processes than natural selection. Typically, the one we will be interested in to address your question is genetic drift.

What is genetic drift?

Genetic drift refers to the random sampling of a population in order to build up the next generation population. There are different ways to model genetic drift (Wright-Fisher model, Moran model, coalescence model) but without having to talk about the details of these mathematical models, it is important that you can conceive the role of random sampling in the change in allele frequency through time. For this, I invite you to first read Why is the strength of genetic drift inversely proportional to the population size? and when you have finished, come back to this post.

One the below figure, you can see the effect of drift through time. The below graph consider a bi-allelic locus (a locus where 2 and only 2 different alleles exist in the population) starting with an initial frequency of 0.5 (=50%). Each line is a separate simulation and shows the frequency of only one of the two alleles.



The above graph considered a population of size $N=100$ individuals. Below, the same types of simulation with a population size of $N=25$ individuals. As you can see that the genetic drift is stronger 



Every single locus is subject to genetic drift whether it is under selection or not. However, if a locus is under strong selection, then genetic drift with have little power to explain what allele will get fixed in comparison to when the locus is neutral.

Genetic drift and loss of alleles

It is clear from the graph above that genetic drift also wipe variant out of the population. We just don't know for sure which variant will be wiped out. To be more accurate, the expected heterozygosity due to genetic drift is reduced by a factor $\frac{1}{2N}$ each generation. One can make plenty of calculations from basic models of genetic drift. For example the expected time to being wiped out is $\bar t(p_0)=-4N\left(\frac{p_0}{1-p_0}\right)\ln(p_0)$, where $p_0$ is the starting frequency of the allele of interest.

A interesting result is that the probability of an allele to reach fixation is equal to its frequency. If there are $N$ individuals in the populations, there are $2N$ alleles (but not $2N$ different alleles). If there are, say 235 alleles A in the population and $2n - 235$ alleles B in the population, then over the long run (so that one will necessarily fix) the probability of fixation of the allele A is $\frac{235}{2N}$ and the probability of fixation of the allele B is $\frac{2N-235}{2N}=1-\frac{235}{2N}$.

Wisdom teeth

In your question, you are interested about a supposedly purely neutral locus. You talked about wisdom teeth I suspect more as an example rather than because you are interested to this trait.

Let's assume that the presence of wisdom teeth is completely neutral. Note by the way that as a rule of thumb if $2 N s &lt;&lt; 1$, (where $s$ is the selection coefficient on a given allele) then the allele will behave essentially as if it was a neutral allele. So, if wisdom teeth is neutral, then the probability of this trait to disappear over the long run depends on the frequency of the allele causing this trait. So far, I have assumed that we were interested in a single locus only. In reality, variation in many traits are caused by variation at several loci. In such case calculations are a little less straight forward (but still feasible). I do not know the genetic basis of wisdom teeth, so I cannot make good predictions for the evolution of this particular trait.

Other evolutionary processes

Here are a few example of interest

Gene flow

Note of course that there are other processes to consider when trying to predict the fate of a given allele or trait. For example, in a given population you might have a flux of migrants that come from a population where one allele is fixed therefore affecting the allele freuqency in the focal population. This is called Gene flow.

Hill-Robertson effects

Never forget that a locus is not alone on its chromosome. It is physically linked to other loci and selective pressures at other loci will affect the allele frequency at the focal locus. This is called Hill-Robertson effects.

Mutations

Of course, when a locus is not polymorphic (has only one allele), mutations is the ultime source of variation. When a locus is polymorphic, then it is likely the mutations will have a minor effect on the allele frequency (although it depends on the size and type of locus and depends on whether mutations can make up new functional alleles).

Pleiotropy and covariance between phenotypic traits

Phenotypic trait do not evolve independently. If wisdom teeth is a consequence of the activation of the molecular pathway for resistance to HIV (which it very probably is not), then wisdom teeth will not evolve as a neutral trait. A locus that affects several traits is said to have pleiotropic effects.