In some quests time and completion speed are very important. If you skip some quests that are clearly urgent (a serial killer running free, possible lynching), it will impact the game world. Because of that, you should prioritize some quests so that you avoid unpleasant consequences. Below you will find a list of timed quests, which you should complete first.
Stay of Execution (Sagus Cliffs)
If you don't help Ris, he will be executed.
In the Circus Manor you will encounter Ris. He is a friend of Tybir. He is in the middle of a trial and on his way to be executed. If you wait too long, he will be killed and it will be impossible to complete the quest.
Circles in Red (Sagus Cliffs)
If you choose wrongly or you won't investigate the murders, new victims will appear.
In this quest you need to establish who is the murderer. If you select Mallet or G'zei, they will be hanged - however, they are innocent. Kiyatawa is the murderer and you should pick her. If the woman remains at large, new murders will occur - random npcs will die, including one of the merchants.
Supplement: Traveling to other parts of the game world
In addition to the abovementioned time-limited quests, you must be aware of the fact that progressing in the main story and traveling to the next location of the game world might cancel the current side quests. In that case you will permanently lose the possibility to complete these quests and to obtain the quests related to them. Such "places of no return" are listed below. Before you move forward, make sure you completed all quests and other side activities (for example, you bought unique artifacts from the traders).
Try to complete all side quests in Sagus Cliffs before you decide to travel on the airship during the conversation with Master Rennio in Caravanserai (M7.2). It is part of the main quest On the Builder's Trail.
Try to complete all side quests in the Valley of Dead Heroes and Necropolis before you take Mazzof's Merecaster from Aadiriis. It happens during the main quest the Sanctuary of Miel Avest in the location of the same name (M14.5).
Try to complete all the side quests in Bloom before you go to talk again with Memovira in Memovira's Fortress after returning from Heart Interior (M24) during the main quest Into the Depths.