Globular clusters occupy an interesting place in the spectrum of composite stellar systems. As you point out, they are highly concentrated populations of stars, and seem to lack any dark matter component, unlike more massive dwarf galaxies.
Binary interactions become very important in simulating globular clusters, and interestingly enough (maybe unsurprisingly), the one example of a discovery of a planet found in a globular cluster has been around a binary star system (see: PSR B1620-26 b; this circumbinary planet was found orbiting a pulsar and a white dwarf.). This is not to say there are not other examples, however, this was the easiest for me to come across. I would be interested to know how common this situation is, and in addition, how stable it is given the potentially highly chaotic environment it lives in. These speculations don't answer your question, but I thought it interesting enough to bring up as evidence in favor of your question not being an unreasonable one to ask.
From the wiki page:
Globular clusters can contain a high density of stars; on average about 0.4 stars per cubic parsec, increasing to 100 or 1000 stars per cubic parsec in the core of the cluster.[26] The typical distance between stars in a globular cluster is about 1 light year,[27] but at its core, the separation is comparable to the size of the Solar System (100 to 1000 times closer than stars near the Solar System).[28]
This seems to indicate to me that location within the globular cluster would matter quite a bit. If at the core the average distance between stars is about three thousand times closer than our nearest neighbor is to our sun (my estimate to give some perspective: a few lightyears to Proxima Centauri divided by 100 is about 3000AU (about 100 times further than Pluto from the sun)), then stable orbits may be shifted inward, or simply may not exist due to two-body interactions.
However, if life were to exist (an assumption we're going to make for the purposes of your question), one would see a very different night sky. According to this paper, the number density profile of stars within the globular cluster M92 follows a Wilson Profile fairly well, which has the form:
$$ f_{W} = A\{ e^{-aE} - e^{-aE_{0}} [1 - a(E-E_{0}) ] \} $$
where $E \le E_{0}$. E is the specific energy of the star:
$$ E = v^{2}/2 + \Phi(r) $$
and where $\Phi(r)$ is the mean-field gravitational potential, determined from the Poisson equation. For each family of models, the constants A, $E_{0}$, and a in the above distribution function define two dimensional scales (a typical radius and a typical mass or velocity) and one dimensionless parameter, the central depth of the potential well (related to the concentration parameter) (all of the information is taken from the paper I've linked).
It seems to be the case that globular clusters are not "simple stellar populations", in that they are usually made of multiple generations (sources: 1,2). However, globular clusters generally consist of population II stars and are older stellar systems when compared to other star clusters. I bring all of this up because in addition to the number density of stars, the stellar distribution of stellar types would certainly be an important factor in how the night sky would look. If you lived a thousandth of a lightyear from a blue supergiant, you could imagine that that would make a huge difference in what you would see on a day to day basis. At the same distance, a supergiant star is on the order of $10^{5}$ times the luminosity of our sun (and therefore is $10^{5}$ the flux, since $L \propto f$ holding $D_{L}$ constant). At the same distance as our sun, the magnitude of a star with $10^{5}$ times the flux would have an apparent magnitude of about -38 (I used Rigel as my test case; this produces a star in our sky which is 12 magnitudes brighter than our sun). Moving this to the average distance between stars at the center of a globular cluster we would get an apparent magnitude of:
- $M = -6.43 $ from $m=-38$ at distance of $d=1$AU.
- $m=-26.43$ from $M=-6.43$ at a distance of $d = .00326 ly$ (the new average distance between stars at the center of a globular cluster)
In other words, a blue supergiant at an average distance between stars within a globular cluster would appear to be as bright as our sun is to us! This is absolutely crazy. Depending on where it is in relation to the sun, it could effective cause two days, or potentially one day which is greater than half the time it takes your planet to rotate once. I would image that this would certainly interfere with observing in optical (and shorter wavelengths).