Watch Crystals   
The crystal refers to the glass that is used in the watch.  There are three main types of crystals that are used in watches:   
(1) Plexi/Acrylic - this is a fancy name for "plastic".  It is highly shock absorbent, and the least likely to break/crack out of the three types of crystal.  Unfortunately it's strength is also it's weakness - a plexi crystal scratches easily.  Plexi is also very cheap - a standard replacement should only be around $15.   
(2) Mineral - more scratch resistant than Plexi, but can break.   
(3) Sapphire - virtually unscratchable, but can break if it receives a very hefty shock.  It is also substantially more expensive.  Most luxury watches will have sapphire crystals. 

Bracelets, Clasps & Bands   
I personally prefer bracelets to leather bands.  Leather ages/degrades faster, and feels less secure.  Plastic/Nylon bands are even worse - and don't allow your wrist to breathe.  The bracelet should have reasonable gaps between the links so that it doesn't pull hairs.  And reasonable gaps also allow your wrist to breathe more.  Most clasps perform their function adequately, but my favourite would have to be the latest Omega Seamaster which has a small push-button safety clasp, and is constructed from solid metal.  Titanium is an excellent material for watches - especially sports watches - it is reputably very strong, and much lighter than stainless steel.   

Movements   
"Movement" refers to the main "time keeping" mechanism inside the watch.  A watch manufacturer makes their watches by either: 
(1) buying a standard movement from another company (e.g. ETA), and then they usually re-furbish/modify the movement to suit their particular needs; or  
(2) manufacture the whole movement "in-house". 
A watch based on a standard movement is more likely to be repairable locally - and at cheaper cost.  However, this is also a "collecting" hobby - so rarity & individuality is important. 

Finishing  
"Finishing" refers to the presentation, attention to detail, and final touches that the manufacturer has done to the watch.  It can also refer to the different surface textures that have been applied to parts of the watch (e.g.. polished or brushed).  In most high end watches the connoisseurs pay close attention to the details of the finishing of the movement.  This even goes as far as alignment of screws and the consistency in the depth of the engraving.  It DOES sound like "nit picking", but in general, the quality of the finishing is reflected in the accuracy and reliability of the watch.  As far as external finishing of the watch case & bracelet - I prefer a polished finish.  The polish shows scratches, but "ages well". 

Dial & Hands  
The dial & hands are the most important part of the watch - since they are the markers which you use to read the time of day.  The hands & markers should stand out on the face so that you can see the time at a glance - even in bad light.  An excellent example of this is Omega's Speedmaster Professional. A shiny metallic dial usually adds more reflections - and so makes it more difficult to see the hands.  I prefer a sweeping, centrally located seconds hand rather than a small seconds hand located on a sub-dial.  This is simply because I think that the dancing movement of a mechanical seconds hand is one of it's greatest assets and I find it positively mesmerizing.  Especially when compared to the "quantum" style of movement of quartz watches.  A quartz watch makes me feel as if nothing exists during a second - and that time is continually jumping to the next second instantaneously.  Time doesn't move in "quanta" (discrete jumps) - it flows like a mechanical watch seconds hand.  

Accuracy  
If you know your watch like the back of your hand (hah!), then you will know how to keep it very accurate.  The accuracy of a standard mechanical watch is known to vary with how the watch is treated.  The watch should generally be fastest when positioned horizontally with the dial up.  And its performance will probably slow by varying amounts depending on whatever other position you may put it in.  With a bit of devotion you can track the performance of your watch in the different positions - and then devise a routine to keep your watch at close to perfect time.  To do this you will have to do some groundwork - spend some weeks comparing & writing down how much the watch has gained or lost overnight, and at the end of the day.  You will then learn how to make your watch gain/or lose time.  If your watch loses 5secs after 14 hrs on your wrist during the  day, then you may be able to correct that by positioning the watch so that it gains 5secs each night.  Your final routine may be something like (1) wear the watch to bed every second night; or (2) leave the watch dial up each night.  If the watch performs too wildly to be able to use this method - then you should probably consider getting it serviced, or regulated. 
My watch was generally averaging +1 to +2 seconds per day - that means a maximum of a couple of minutes fast per month.  So I don't even bother with a routine - I'll just adjust it every couple of months. 
Watches that have a Chronometer Certificate have passed stringent tests to ensure that they conform to defined limits of accuracy no matter what position the watch is in.