There are many challenges to researching an historical fiction novel. Firstly, I'd like to state that research is no stranger to me; I've been happy researching for decades, be it Roman, Anglo-Saxon, pre-history, Medieval or later. My degrees are in earlier periods (predominately Early Medieval England, Scotland and Ireland) and I have been working in Tudor buildings or re-enacting Tudor era since before the millennium. Yet I still faced many challenges. Research for some is a joy and for many it simply includes picking up a few basic history books and looking up wiki facts (which I don't condemn at all – even wiki can help a researcher by listing references below which can be followed up. It's an excellent starting point for a new researcher, but do be aware that facts are sometimes incorrect on wiki and should be used as a compass point and not an actual reference).
But there is another type of research, infinitely more fun and rewarding; and that is to go out and do your own primary research. Visit the British Library if you are able, see for yourself the manuscripts that the historians are using as the foundations of their history books. Go to those castles and photograph like mad (if permitted, if not, just get a feel for the place and take copious notes) to understand exactly how your characters, historical or fiction, would be interacting within those stone walls. Visit every museum you can that holds artifacts from the era you are researching and talk to other researchers.
Researching for the 16th century for A Corpse in Cipher was incredibly enjoyable but it was certainly fraught with challenges. For one, many of the history books of the Tudor era are heavily Elizabethan biased. Assumptions seemed to have been made on this that project later Tudor living onto the earlier. Although Anne Boleyn is a vigorous subject both as Elizabeth's mother and in her own right, I've noticed histories focus on her experiences and her husband's without much regard for era details outside of the bedchamber. General Tudor history books will try to encompass early Tudor living, but it is still based on the Elizabethan (and Henry's sex life). This is a pitfall into which many new writers can fall; relying on generalized histories that do not concentrate specifically on their era.
Which brings me to the second challenge – money. Unless you have a university library to hand filled with books belonging to your research era, the necessary books will need to be obtained via cash means. Even with good research libraries at hand (lets face it, public libraries just aren't going to have that rare copy you're after nor will they purchase it at request), photocopies for books that mustn't leave the property can add up. So can photograph permissions and publishing rights. It all adds up. E-bay is a beautiful thing for books. I've found some rare treasures on e-bay that years of searching dusty old second hand shops have yet to yield. As most writers are poor, doing accurate research is going to be expensive.
There are many more challenges, but I'll just sum up the next two here, and that is distance and status. I was lucky enough to be living in England (fortuitously just an hour north of London on the train, which put me in an advantageous physical location as I was surrounded by Tudor era buildings all within an easy drive or bus ride) and I know that others don't have that advantage and 'getting there' is going to be more costly than the acquisition of the right books. And of course, just like when I attempted to arrange a meeting with the assistant curator of Castle Howard to view some Tudor era letters, I lacked enough clout to be taken seriously (why allow a writer of fiction books access to fragile documents, it's not like it's a 'research degree') and there were many, many others who gave the same cold reception. Of course, it may have helped if I'd first prepared a letter of introduction from someone high up in the field. Then again, it may have proved to be just as fruitless. Without the backing of a university (an active backing, as postgraduate alumni don't seem to matter), those doors just keep being slammed.
The good news is that there are many enthusiasts within each research era that can give reference pointers (don't ever just take one person's word for it – do the research! I've met some lovely people online and at re-enactments who are still hanging onto some outdated theory or disproved 'fact'). There are also online histories that have transcribed documents and made them available to the general public... for free. With the right timing, wording, and yes, introductions, some museums and research centers will respond with tips, facts or even invites for viewings, but expect many doors to be slammed in your face first if you're not carrying a postgraduate research degree badge. It's not an easy life-choice to make, but doing the proper research for your book will make it more believable not just for your readers, but for you. And if you happen to discover something new that the historians have overlooked, don't hide it away, share it. It may just open a few more doors...