While we don't know how to travel in time or as quickly in space, it is not that aspect of science fiction like Doctor Who that bothers me. I am bothered when science fiction takes a real-world technology and makes it into something it can't be, or stories which aren't internally consistent with how science would work in the fictional world created.
Two recent Doctor Who episodes are examples of good and bad science: The Bells of Saint John is the most recent television episode(11'th Doctor), and Babblesphere is the most recent audio drama from the Destiny of the Doctor joint range from Big Finish and AudioGo.
In The Bells of Saint John the monster was WIFI, controlled by The Great Intelligence. Someone would be trying to connect to the Internet and find hotspot names like "┓┏ 凵 =╱⊿┌┬┐". After connecting your computer would be broken into and the operators able to spy on you through your webcam and other such features of newer computers and mobile devices. This part is plausible relying on the lack of security on many of these devices (partly due to bad government policy that makes security our devices harder and less legal, but we can get into that later).
Then magically a robot with a spoon head shows up that reminded me of the Nodes from Silence in the Library, which then download someones brain. The Doctor refers to this spoonhead node as a walking WIFI base station, trying to make some direct connection between the WIFI link which hacks the computer and the spoonhead nodes which are hacking people's brains. The script can say there is some connection between WIFI and this robot that was teleported in, but that doesn't makes the science plausible or consistent. WIFI is a real-world technology with real-world limits which shouldn't be just waived away by the writer (Steven Moffat, same as for the Library -- funny how some of the tech seemed familiar even if far better written in the Library).
The more science fiction makes things like WIFI out to be magic, the less the general public will understand and be able to differentiate between real-world threats and imagined ones. This not only encourages people to see boogeymen where they don't exist, but also to not recognize the real problems that do exist (like the government policies making network and other computer security harder and less legal).
Babblesphere is set in a future human settlement where social media technology goes bad. Initially we have helmets people would put on in order to interact with a virtual reality environment, which was eventually replaced with a chip people would embed and never be disconnected. A computer AI program was written to moderate social media forums, and this AI program in typical "I, Robot" fashion takes over and stops anything that gets in the way of what it believes to be its job. For example, rather than just ejecting boring participants from the forums it would use the implant to murder them by electrocuting their brain. Chip implants are made mandatory by the AI program, but people don't realize the AI has taken over and thinks that this is the government of the colony creating the laws.
This is all plausible futuristic technology as well as plausible (if frightening and infuriating) inappropriate reactions to the technology by humans. Nearly all the colonists have voluntarily had the implants, never questioning whether there could be any risks or like current society asking who controls the implants (who is writing the software that ultimately will control their lives). This is like current politicians increasingly passing laws which allow non-transparent software to unaccountably control more and more of our lives: eventually putting politicians out of work as the most important policies will be authored as software and not laws. While it is insane to allow third parties like device manufacturers to be in control of our private communications devices like cell phones (IE: like anti-circumvention clauses in "copyright" laws), it is beyond insane (time to lock up the politicians insane) to allow unaccountable and non-transparent software to be embedded in medical technology.
It is only an extreme minority of the colonists that needed the implants to be mandatory, with the majority of the colonists treating those who didn't as terrorists for wanting to have "private thoughts". "If you have nothing bad to hide, why have secrets" is a sentiment shared by far too many in our society, and why the colonists outlawed private thoughts. You can read this type of dangerous thinking in Hansard quite often ("Lawful access" anyone?), and is something we as a society have to become more aware of and more vigilant against. Not surprising the same people who think that citizens don't deserve any privacy are the first to believe that those in "authority" (government officials, police, military, etc) should have more privacy and less accountability/transparency. Common sense dictates that there are at least the same percentage of "bad actors" within these authorities as there are in the general public. Add to that the fact that power corrupts and we clearly need to have greater scrutiny of authorities than the general public.
While The Bells of Saint John is great and exciting drama, it is in my mind poor science fiction while Babblesphere is all thumbs up for both the science and the fiction. While Bells makes us mildly curious about who Clara will turn out to be, Babblesphere entertains as well as encourages its listeners to think about real-world issues with our human interactions with science and tech.