My main problems with Jinteki are:
1) When I play against Jinteki, they will often trick me multiple times during the game. (Running into trap, or my choosing not to run an agenda because I thought it was a trap). You would think this would look like a Jinteki win, however I still tend to beat them easily. Jinteki is like: "hehe I tricked you", and I'm like: whatever I won.
2) Its hard for Jinteki to put up a decent defense, that isnt reliant on 'if you run into a trap you could be screwed'. Their ice just isnt very suited to actually defending. This is mainly a concern with guarding central servers. The remote could be a trap, so bluffing can 'guard' things there. But for centrals, as long as I can withstand running into a Snare or Fetal, I'm fine. Good runner decks attack centrals hard. Jinteki tends to fold to the pressure.
3) Its too easy for Jinteki to be poor, and have to click for money. A corp that clicks for just $1 a click too often, ends of being too slow and getting its centrals destroyed before it can advance enough agendas. This problem is made worse by the fact that Jinteki has to pay for traps. Snare costs 4, which can really hurt. Often the runner spends a turn recovery, but so does Jinteki, so the net gain was basically nothing, if they didnt die.
4) Damage which doesnt result in a kill, tends to be inefficient. Sometimes you get a key card with it and its great, but more often a decent player will put out his critical cards first, draw up, and then run with cards he doesnt mind losing. When he takes damage, if essentially frees up hand slots to draw again, looking for the best cards, without having to discard wastefully.
Nonlethal Junebugs are pretty expensive for the corp. For example, a 2 advance Junebug costs 3 clicks and $3 for the corp. (Install, advance, advance, pay 1 to activate). If the runner broke 1 ice and took 4, then he probably didnt lose any more than the corp did.
5) Its agenda mix is probably the weakest of any faction. HB has a pair of strong 3/2 agendas. NBN has the crazy Astroscript, plus the amazing Breaking News. And soon to add Beale. Weyland has the awesome Project Atlas, and also Hostile takeover is nice. Jinteki has:
Nisei. Its awesome. But its a 4/2. Everyone else's best agenda is a 3/2. Nisei is best with a strong remote fort, which is a thing Jinteki is kindof weak at.
Braintrust. This is the worst 3/2 in the game. It is basically blank. Its still a good card, but its just not as good as the other 3/2s.
* Fetal AI. Basically, this is an agenda you dont want to score, since if you do its 5 advances and $5 for 2 points and no ability. Everyone esle would get 3 points + ability for that. You basically want the runner to hit it and lose 2 cards and $2. But thats not great either because they got an agenda. Basically, this card either results in a kill, or kindof sucks. Its pretty much only good if you can trick them into slamming into it without money to score it, taking a free 2 damage.
In the end, Jinteki tries to trick you, but gets insufficient reward for succeeding. It doesnt have the good economy tools, or defense tools, to play a strong game. Other decks can fool you also, like Weyland getting you with a trap because you thought the double advanced card was Posted Bounty or Government Contracts. Or HB/NBN putting a card face down, threatening a 3/2 agenda, but when you run it you lose money and then its just a Bernice Mai, or SanSan, or whatever, and youre out a lot of money.
When those decks trick you, and you lose lots of time, the back it up by using their economic lead to power ahead. But when Jinteki tricks you, if you arent dead, then Jinteki was set back a lot by his buff, because he just lost a 2 advanced Junebug, or $4 for the snare. Whereas Weyland made you break a Hadrians Wall and another ice to get in to that Secretary, and wrecked you, Jinteki had weaker defenses due to low economy and weak ice. So you arent as far behind. Jinteki might push through an agenda while you recover, but if he does he is even poorer, and its time to smash his centrals.