How much does time-dilation effect our observance of the most massive objects in our solar system? Disclaimer: I'm kind of a newb, so I apologize if this question is not well formed. Please comment if anything is unclear, and I will do my best to make corrections.
Reading this post about time dilation near the sun, I wonder if in the videos I've seen of either solar events (like solar flares) or Jupiter where we are observing Jupiter's Big Red Dot storm, and I'm wondering if I was viewing a slightly skewed perspective because of time-dilation? And if there is any advantage or disadvantage to this perspective? Specifically...
A. If what I saw was actually in a time dilated frame of reference where solar flares appear in "slow motion", or sequential pics of Jupiter from the Hubble are moving more rapidly than say footage from Voyager -- which was shot at relatively the same distance from the sun and therefore should match Jupiters relative frame, or if the dilation was negligible?
B. Are there any cases where we are (or might be) in an advantageous frame of reference to observe cosmic events, where we glean more data because we can observe these events "faster" or "slower" from our view point?
 A: An event that occurs on the sun, such as a solar flare, will have a slightly longer duration when observed from earth compared to the duration it would have if the observer were on the sun. The difference is tiny, though: an event that lasts one hour on the sun would last one hour plus $7$ milliseconds when observed from earth. Similarly, an event that lasts one hour on Jupiter would last one hour plus $0.07$ milliseconds when observed from earth.

...I'm wondering if I was viewing a slightly skewed perspective because of time-dilation...

Yes, slightly, but probably not noticeably, unless you're making some pretty precise measurements.
By the way, an event that lasts one hour on the sun would still last exactly one hour if observed from the "surface" of a distant star having the same mass and radius as the sun, because in this case, the event and the observer are both subject to the same gravitational time dilation. In contrast, when an event on the sun is observed from the earth, the earth's gravitational time dilation is insignificant compared to the sun's, so the sun's effect is not significantly compensated by the earth's.
When comparing to Voyager's observations, we also need to account for Voyager's motion; but again, the effect is tiny. (I haven't done the calculation, but the fact that Voyager is moving much more slowly than the speed of light implies that the effect will be tiny.)

Are there any cases where we are (or might be) in an advantageous frame of reference to observe cosmic events, where we glean more data because we can observe these events "faster" or "slower" from our view point?

In cases where time dilation is large enough to be advantageous, the observations would be complicated by the fact that the light itself (by which we observe the events) is also time-dilated, aka redshifted. So even if we could observe an event on the surface of a very massive compact object with a the time-dilation factor of $1,000,000$, the light from that event would also be redshifted by a factor of $1,000,000$, so light that would have been visible (wavelengths $\sim 400$-$700$ nanometers) would be received with radio wavelengths ($400$-$700$ millimeters). We wouldn't be able to see it with our eyes, but we could still observe it with the help of appropriate instruments.
A more severe complication is the fact that the most compact non-black-hole objects we know about, namely neutron stars, have time dilation factors $\lesssim 2$, nothing close to $1,000,000$. 
Another complication is that we are much too far away from such objects to resolve things spatially. We can't even resolve the sizes of distant stars spatially, much less things that are happening on the surfaces of those stars. We'd have to get much closer to resolve such things spatially, and that means we'd have to take a very long journey to get there.
Despite these complications, we apparently have observed the effects of significant time-dilation through the redshift itself. As reviewed in [1], matter near black holes is expected to be bathed in high-energy X-rays, which can cause matter near the black hole to fluoresce. The most prominent example is iron, which has one fluoresence line with an energy of $6.4$ keV (which is in the X-ray part of the spectrum). This spectral line has been observed near supermassive black holes in the centers of galaxies, where it is smeared out into significantly lower energies ($\sim 20$% lower), presumably as a result of a combination of relativistic Doppler and gravitational redshift effects. But this is "only" a $\sim 20$% effect. It's significant, but it probably doesn't have much use in terms of watching things happen in slow motion. 

[1] Reynolds and Nowak (2002), "Fluorescent iron lines as a probe of astrophysical black hole systems," https://arxiv.org/abs/astro-ph/0212065
