There are few things I would actually use for research, mostly, given that I enjoy the history of food and dining the most, I tend towards original documents. This isn't an argument about primary, secondary and tertiary sources that we could easily get caught up in and lose the original point being made here. This is about using something made for the reason of modern entertainment, though they feature some historic study, a documentary is still subject to entertainment first... they need to arouse us and get us watching, they need to sell themselves to broadcasters as something entertaining and what they do not need to do is cite all their sources or back up everything presented to us.
This comes back to a little film called "A Tudor Feast at Christmas", released in 2006, where people are gathering items for a presumably 1590s dinner from a lush garden with a Peacock pie (obscuring the pie) and sillibub... where freelance historian Ruth Goodman says:
"courses as such didn't really exist at this point, you have removes, so you fill the table with food, and when everyone is finished eating it, you remove it, and that's one remove. And you fill the tables again and usually it's no more than two removes, it's very unusual to go to three."
So here we are given all this information by what the documentary tells us are "experts" so who are we to disagree?
Of course, I might point out that she never says they called them "removes" but rather calls them this herself to differentiate her modern vision from the period vision which really is not different, a course being several dishes being served together. What this really sounds like, to me anyway, is the someone trying to differentiate between services, which is how the food is served. My 1960s Betty Crocker book (yes, I was looking for something modern), for example, lists two types: one called "Russian" where a servant delivers individual dishes to the table, and "English" where courses are served out to the table and administered from there. The 1590 equivalent is not much different than this, where a servant may bring food to the table, set it, and may even carve it at the table (growing less common by this time according to a book on servicemen of the period, for which sadly I can not remember the title on writing this). After this point, another "course" of food would be brought to the table, and so on. She is correct about the number of "courses" however, though by this time, the banquet had begun to start in popularity which could add a third.
On "remove" however, I tend to react because of it's frequent use in groups such as the SCA to describe a course of food for the table, I know not of it's use by the "Tudor Group" for which this person belongs. The problem I have with using the word to describe an early course of dishes is that the word already has a use to describe a replacement of a dish within a course. While I can not give you the earliest recording of this, I have not seen it prior to the 17th century but have seen it afterwards, but regardless, the very suitable word "course" is already present for our use.
Fun tidbits on a 1590's feast in England, not a whole lot was seasonal... The best meat would be pork, the best dishes including the Brawn which would have a secure standing of being the first to be brought in. Baked, and even roasted, Turkey was gaining popularity, it is even compared often to Peacock and if we were to look at post period paintings, we can see the outer form of a Turkeycock displayed on top of a large pie (there are examples of the same for peacock) though I don't have much by good evidence of this display appearing in 1590 so it's guesswork there. Another very seasonal food were oysters, said to be in season year long... many other foods, if they could not be had fresh, came preserved.
An item I also would like to touch is the Silibub, I do wish they shared their source and can only hope it came from a manuscript rather than published works, because between the two, the earliest I could find was from the 1620's. A posset curd would probably have been a better choice being well documented to that era.
But... don't take my word, read through some books written in the period, look at some art, view some artifacts, play with your food... have fun!
EDIT: I managed to get an awesome reply on the Silibub, as stated I hoped that it had come from a manuscript of some sort because I lacked any actual recipes from the period and only as early as the 1620's.
In the response were some of these sources: (yay for the OED! and P. Troy, hope you don't mind some sort of credit here)
-"c1537 Thersytes (1848) 79 You and I..Muste walke to him and eate a solybubbe."
-1570 in J. J. Cartwright Chapters Hist. Yks. (1872) 55 They brough this examynent a selybube to drynk.
-1584 T. Cogan Hauen of Health cc. 166 A posset or Selibub made of Verjuice, is good to coole a cholerick stomacke.
-1601 P. Holland tr. Pliny Hist. World I. 348 They vsed to thicken their milk into a kind of pleasant soure curd in manner of a Sellibub.
-1591–2 ‘A. Foulweather’ Wonderfull Prognost. in Wks. (Grosart) II. 165 Maides this quarter shall make sillyebubbes for their Louers.
-1602 in Lyly's Wks. (1902) I. 492 First you shall haue a dayntie sillibub; next a messe of clowted creame.
-1598 J. Marston Metamorph. Pigmalions Image 60 Ye Granta's white Nymphs, come & with you bring Some sillabub.
I especially enjoy the mentions eating a sillibub in the earliest mention, though it would also be drunk, a posset was also mentioned, quite often, as something you would eat... much like we would a junket which is curdled with rennet.
And this my friends... and random people I don't know, is why I encourage further reading!