The disconnection of networks is explained in the miniseries that starts the reboot - the Galactica was one of the only remaining warships that was not networked - and this is what saved it from the malware portion of the Cylon attack.
The newer ships, connected using some sort of advanced networking, were infected by the Cylons, and so destroyed.
Some humans knew that technology could - maybe must - lead to the destruction of their race, e.g. by creating the Cylons (workers who later devastatingly rebelled).
As such, there was distrust of advanced technology - Adama, in particular, expresses this a lot early in the series (he had a lot of experience with the Cylons from the earlier war).
The Galactica was his command (for around three years prior to the start of the series), so the lack of the most recent technology makes sense.
In addition, the Galactica was 50 years old -
it was about to be decommissioned as the series began.
As a result, the technology on board was not as recent as that on the colonies - and this was supplemented by what survivors of a genocidal attack happened to have.
They didn't have time to develop or build new technology during the events of the series, or foreknowledge to pack every high-tech device they might need aboard these ships.
scifi.stackexchange.com/users/108/Tony Meyer
I can't remember where I saw it, might have been a behind the scenes show on sci-fi channel, but there was an interview with Moore that he talked a few minutes about the tech of BSG.
He explained that one of the goals of the reboot of BSG was to keep the technology simple and close to current day "realistic" idea of technology.
Obviously, they had to fudge some stuff with FTL drives and the likes but otherwise he said they didn't want technology to get in the way of the story.
scifi.stackexchange.com/users/1443/Alan Barber
Apart from being old.
Galactica was designed that way.
Because Cylons are machines they can easily use and manipulate advanced technology (so the theory goes) Because of this Galactica was designed with the lisede technology possible so it can do the job but nothing more so it is relatively safe from the Cylon interference.
It is not even networked so even if its captured it will not contaminate other ships.
scifi.stackexchange.com/users/1406/Sinan
Was anyone here actually impressed with any of their spaceships?
None of them were built for anything beyond a cruise around the 12 Colonies.
None could handle long duration missions.
And with the exception of the two warships we saw (Galactica and Pegasus), none of them were any good at handling battle damage.
It looked to me like their space technology was fairly immature.
They no doubt retained some of the technology they had at the time of the founding of the Colonies (some of which may have come from the Lords of Kobol), but I don't get the impression that their technology advanced very much after that, until recently.
In fact, do we have any reason to believe that they came from Kobol in FTL-capable ships?
They may have only developed FTL in recent centuries, and it clearly wasn't cheap enough to put on every ship, "just in case".
scifi.stackexchange.com/users/250/John Saunders
We know nothing about their FTL technology -- maybe it is fairly simple, either because this is a property of BSG universe or just we are missing something obvious (there was a short story about Earth being attacked by antigravity-
and FTL- capable creatures of an overall middle ages level, but I can't recall the title now :-( ).
Also, the technology development path is rather a tree than a ladder -- some branches may greatly overtake the others, especially with some directed stimuli (for instance rocket technology development during the cold war).
scifi.stackexchange.com/users/None/
One simple explanation could be economics and expectation.
It could perhaps be very expensive/uncommon to build portable weapons out of plastic, so you expect x-ray machines to be able to detect almost all weapons.
Similarly, you may not expect infiltration from enemies so your security apparatus may be geared toward heavy-duty attacks.
Remember that even the military has to pay in one form or another for things it builds and operates, so they prefer inexpensive things like cables instead of wi-fi.
scifi.stackexchange.com/users/947/apoorv020
The galactica was the oldest remaining ship in the colonial fleet at the time of the attack it was 50 years old the computer systems were neither networked nor integrated during these refits due to the fears of its commander, William Adama.
Due to this lack of network integration at the time of the Cylon attack, Galactica was unaffected by the infiltration program used by the Cylons to disable Colonial vessels and defense systems, using the Command Navigation Program (CNP), developed by Dr. Gaius Baltar and subverted by Cylon operative Number Six as a back door into such systems.
scifi.stackexchange.com/users/24388/user24388
On one hand, residents of the Twelve colonies perfected travel in spaceships and FTL jumps, but on the other hand, they have some really low-tech technologies, such as disconnecting a network by pulling at a lot of cables [ 1 ], or having no better way of checking for weapons other than the x-ray machines [ 2 ]. Can that be explained by something other than flawed writing?
Why is there a lot of low-tech in Battlestar Galactica?
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<technology><battlestar-galactica><spaceship>
scifi.stackexchange.com/questions/2795
scifi.stackexchange.com/users/1439/Innab
Adama expresses a distrust of advanced technology early in the series. In addition, they may not have had time to develop or build new technology during the events of the series, or foreknowledge to pack every high-tech device they might need aboard these ships. Also, one of the goals of the reboot was to keep the technology simple and close to current day "realistic" idea of technology.  One theory is that because Cylons are machines, they can easily use and manipulate advanced technology. Therfore, Galactica was designed with the least technology possible so it can do the job but nothing more, making it relatively safe from Cylon interference. The idea of Battlestar Galactica was to keep technology "realistic" for its then audience. In the show, there was distrust of technology. Moreover, the Cylons, being machines found advanced technology easy to manipulate. However, they found low-tech mush more difficult to infiltrate. 
There was distrust of advanced technology and there was also no time to develop new technology the events of the series. The idea of the show was to keep the technology "realistic" for the current day audience. Technology could be expensive and they only built what hey thought they needed. The Cylons were machines and thus could easily manipulate advanced technology. By keeping the technology simple, it was more difficult for the Cylons to infiltrate.