Chess shot puzzles are far better when presented in Fritz versus in the static pages of a printed paperback book.

One awful problem with paperback book presentation of puzzles is that paperback book bindings flip the book shut. I hate having to devote a hand to holding the book open. Better is a lay-flat plastic rings binding, such as is used by Ian Anderson in his Chess Visualization Course books.
People tend to feel the rings binding is less classy, but they should rethink that attitude for chess puzzle books.

But the biggest advantage of presenting the puzzles in Fritz mode (loadable as a .PGN of FENs) is that you can manipulate the pieces and position after initial study, to learn more.
In contrast, with a static book you have to spend way too much time setting up the position, and resetting the position when testing variations. Plus you do not have Fritz to tell you what you might be overlooking.

ERROR RATE IN REINFELD: I have used Fritz to check hundreds of Reinfeld's puzzles. I find the error rate is over 10%, which I consider to be very high.

Reinfeld's "1001 Winning Chess Sacrifices and Combinations" has an astonishingly high percentage of shot puzzles that are well geared in difficulty. Some or many shot puzzle books fail in this dimension.
And regarding Stigma's well-received distinction between puzzles that emphasize (a) patterns versus (b) long calculation, Reinfeld does very well at patterns while keeping calculation lengths moderate.

Ray Cheng's far newer book "Practical Chess Exercises: 600*" is successful in the same important way that Reinfeld's book is; despite Cheng's wrongly-applauded mix-in of puzzles with no solutions: heck I guess Reinfeld's 100 errors could be re-marketed as puzzles with no solutions, to keep the student honest!?

I think there might be .pgn files of Reinfeld's puzzles on the web; although maybe no .pgn for Cheng's book.

FIXES NEEDED IN REINFELD

Reinfeld's book is in drastic need of being re-written and re-formatted. Needed changes include:

*** The diagrams are blurry and a bit too small.
*** The answers in the back of the book are physically too far from their corresponding puzzles.
*** A translation of the answers into SAN or LAN or XSAN notation (from old Descriptive) is certainly needed.
*** About 100 errored puzzles should be so-marked or fixed or replaced or whatever.
*** A plastic rings binding option should be made available.

But the guy who currently owns the rights to the book is unwilling to sell the rights.
.

Stigma wrote on 06/06/13 at 15:49:16:

If I had to guess, I'd say 1700-2000 for volume 2 and 2000+ for volume 3. I've only done a few problems from the third volume.

Volume 2 also contains a lot of relatively simple endgame studies, which is nice. It can be hard to find studies that are challenging but solvable by mortals.

I am a big fan of Chess School aka Manual of Chess Combinations (4 volumes: 1a/1b/2/3). Most people here shouldn't bother with volumes 1a and 1b unless they want to drill pretty basic stuff. One nice thing about the earlier volumes especially is that they are very complete, covering every standard tactic and combination comprehensively. It is pre-computer era though.

I don't think Aagaard is fair to chesstempo.com. There are certainly some problems that wouldn't pass a book-inclusion test, but in general they're a testament to automated chess-problem harvesting (the site author has an engine go through actual games automatically looking for positions to use) and the whole site is a real pleasure to use. I do 10 problems there every day.

I looked at this QC blogpost: http://www.qualitychess.co.uk/blog/?p=1815

... and it inspired me to think about which problem sets are best for training. Having them computer-checked by a competent author to avoid faulty and alternative solutions is of course very handy, and I expect most modern exercise and calculation books to be well-checked (certainly from publishers like QC and Gambit). 

On the other hand, the two tactical excercise sets I've used most obsessively, Reinfeld's two "1001" books early on and now "CT-Art 4" by Maxim Blokh (Convekta), have a number of errors if I'm to believe various comments around the net, and I can't say that has hurt me much. I just make a note of which problems are fishy so that I know which they are the next run through.

Aagaard seems to assume that books will always be better checked and planned than computer programs or websites. Maybe that's the case at the moment, but I don't see any principled reason why it has to be. Working on a computer can have a number of advantages; it's easier to measure rating progress, choose problems according to theme or difficulty, integrate spaced repetition, etc. I've recently started using ChessTempo which seems to be one of Aagaard's targets; the problems there are certainly computer-checked but not chosen according to any deep pedagogical plan. But there's a lot of problems that won't be found elsewhere, so I can live with the occasional "freak" problem with little practical relevance. Too well-known positions is a perennial problem in books, though probably not the ones by Agaard (or other QC books). 

Another problem with books is that many of them try to cater to every chess player and have positions from close to beginner level up to GM level, and few of them indicate a recommended rating range. I would much rather get (or be able to select) problems that are just right for my level.

So which problem sets (in whatever medium) are well-chosen? Which are carefully computer-checked? Which are good for different levels? For a start, here are the ones I currently use, chosen because they have many problems that are moderately difficult for me, at ~2150:

CT-Art 4.0 (program)
- well chosen and organized, but probably not all computer-checked. Grouped by theme or diffculty as desired.

ChessTempo (website)
- computer-checked, but maybe auto-generated? May contain some misevaluations in deep lines? Random order, but roughly right level (can be grouped by theme with a paid account).

Aagard: Excelling at Combinational Chess (book)
- computer-checked, mostly quite challenging for me. All the positions are from games in the Sicilian, this will be a plus for some and a minus for others. Grouped by ECO code (!) and split into "Pattern combinations" and "Calculation Combinations".

Vamos: Chess Tactics for Advanced Players (book)
- not sure how well-checked this is; contains maybe too many well-known old positions, but consistent level; lots of moderately difficult exercises. Grouped by theme.

Pongo: Tactical Targets in Chess, Volume 2: Mate Combinations (book)
- good concept but horrible translation, which makes me suspicious of the accuracy of the analysis too. Haven't found any glaring errors so far though. Grouped by theme. Picked this up because i need to work on attacking play, and adding lots of mating patterns should help.

Williams: Improve Your Attacking Chess (book)
- starts off with some very easy problems in each chapter, but gets trickier quickly. Grouped by broad theme; increasing difficulty within each theme. Recent enough that it should be computer-checked, but I'm not sure.

A whole related issue is striking the right balance between easy problems (pattern training) and hard problems (calculation training), but I will ask about that on the QC blog instead.