Most fans agree that Dragon Ball Super is a worthy successor to Dragon Ball Z, even if it's not perfect. It's certainly better regarded than Dragon Ball GT, the original successor series to Z, which has a pretty poor reputation among fans. However, GT's existence is still considered canon by the Dragon Ball creators at Toei, and that causes some major problems when trying to cram Dragon Ball Super into the timeline.
Dragon Ball Super is clearly set between the end of Dragon Ball Z's Majin Buu Saga and the flash-forward ten years into the future that forms the series' conclusion. A ten-year timeframe would seem to provide enough room to avoid continuity issues, but as Dragon Ball Super has continued, it has gradually moved closer to that timeframe, with Dragon Ball Super: Super Hero supposedly taking place just one year before the end of Dragon Ball Z. With Super still ongoing, it presents a major continuity issue, and one that's unlikely to be resolved.
Dragon Ball Super often conflicts with Z and GT
The progression of the Super story is completely opposite to the old series.
Dragon Ball Super saw Goku and Vegeta reach new levels of power that were almost unimaginable in the Dragon Ball Z era, fight on the level of gods, and train under an Angel and the God of Destruction himself, Beerus. Needless to say, none of this is reflected in GT, which is set after Super despite being set before it. Fans rewatching GT today often have to wonder, “why didn’t Goku or Vegeta just use Ultra Instinct/Super Saiyan Blue/etc to solve this problem?” and the series really doesn't offer much of a solution.
As the newest addition, Super has to make sure it fits in with the previous continuity, and that includes both the next series as well as the previous series. But the problem goes beyond the absence of new forms introduced in Super from GT. For example, Vegeta's character has grown quite a bit over the course of Dragon Ball Super, but that character development isn't reflected in GT at all, as he's still the same as he was at the end of Dragon Ball Z.
If the problem was only with Dragon Ball GT, it could easily be solved by declaring GT as non-canon, which many fans have deemed to be the case. However, Super is also inconsistent with the ending of Dragon Ball Z; most obviously Bulma says in the penultimate chapter of the manga that they haven't seen Goku in five years, which is clearly not true in Super. Vegeta also acts as if he hasn't seen Goku in a while, when in reality, according to Super, they've been training together for years now.
Dragon Ball Super is running out of time to resolve these conflicts
Both in and out of space, Super doesn't have much time to deal with the problem.
With Super Hero having moved Super's timeline up just a year before the end of Z, there's little chance of the series fixing these continuity conflicts. The Super manga is currently on hiatus, but it's believed that when it returns, it will be the final arc of Dragon Ball Super. That means that if these issues are resolved, the next arc will have to be the one that resolves them, and it seems highly unlikely that this will happen.
The conflict between Super and the ending of Z can be explained somewhat; Goku actually spent some of Super in outer space at this point, including most of the Galactic Patrol Prisoner Saga and Granolah the Survivor Saga, and he only returned to Earth momentarily to pick up Gohan in the post-Super Hero chapter. Perhaps Goku and Vegeta were actually mostly off-world during their five years in space, and Goku simply didn't see Bulma on any of his trips back to Earth. Either way, it wouldn't be out of the ordinary for Goku to forget to say hello to his friends.
However, the conflict with GT is much larger and more difficult to resolve. It's simply impossible for Goku and/or Vegeta not to at least mention their godly forms, even if it's not an option for some reason. There's also the absence of Beerus, Whis, and other Superhuman characters who presumably still exist in GT's timeline. For example, with Broly now an ally, where was he during the various crises they faced in GT?
Can Dragon Ball Super fix continuity errors, or should it be considered non-canon?
It is not impossible to fix these problems, but it may be necessary to change the Canon
With the extreme popularity of Dragon Ball Super, it seems like there's almost no way it could be considered non-canon. Being something that was directed by Akira Toriyama, Dragon Ball Super has a much higher chance of becoming canon than GT, so if anything, GT is the show that should be declared non-canon when the two series clash.. Toei seems very reluctant to do this for some reason, but as Super gets closer to the GT timeline, this is an issue they'll have to address sooner or later.
However, there's still the issue of Dragon Ball Z's ending. As part of Z, it would be difficult to simply declare the ending non-canon, even if that were the simplest solution. Perhaps Dragon Ball Super could show a new version of the events seen in Z's ending, one that's more consistent with Super's story, thus providing more of a retcon solution than just completely removing Z's ending. With Dragon Ball Daima added to the mix early on, there could be even more continuity issues that arise depending on when exactly that series is set.
Dragon Ball SuperThe 'continuity issues are definitely a headache to deal with, so hopefully the powers that be will make a decision regarding Dragon Ball's continuity soon.