No offense is intended with the following comments but I thought I would throw in my 2 cents worth.
No offense taken.. I'll respsond as I see it
Battery life / Power requirements. - Most PDAs these days tend to use an internal Lithium battery so your going to need power at each range to keep the PDAs charged as I doubt they will last a day on the range on just one charge.
Actually, it's not that bad.. a lot of PDA's have a sleep mode (that takes less then a seocnd to get out of) . you don't need to leave the PDA "ON" all the time. just hit the power button and it goes into sleep mode until the next competitor is ready to score.. you can last about 2-3 days like that depending on the model you have. Also there are now "batter packs" you can by which you put in AA's and it plugs into your pda for backup power (cost $20. approx).
Weather - We shoot come hell or high water, I dont know how well PDAs will hold up to cold, rain, dust, etc.
That is a very valid concern, and being a touch screen, then PDA can be operated in a bag

(unlike a paper sheet which you need to take out to write on
Shooter score verification - I think most shooters appreciate having their copy of the scoresheet so they can verify their scores at the end of the match. With a PDA thier copy wouldnt exist so they would have to take extra time double checking all the figures in the PDA before signing off, I think this would slow things down on the range and shooters may still not trust the accuracy of the technology.
Thats true but I haven't seen any L1 or L2 which do this, only L3's which use the papers that give the shooter a copy. for L3's you can have a portable printer ($250 give you a bluetooth, wifi battery printer you can have on the range). and you can print the shooter sheet right then and there.
As for the "verification" there is verification that can check the "Stage definition" to make sure that all shots are accounted for on the screen before the person signs it.. no mathmatical errors that can get through.
Small Screen - PDAs have small screens and I dont know how simple life will be for a score keeper or competitor to read the thing, especially on say a bright sunny day.
There are different sizes and prices of PDA's you can get something like the Nokia PDA which is about 3X larger then a PDA phone, and you can see it very easy.
Cost - PDAs are not cheap, if a club or organization was to go this route I could easily see their bill for PDAs and spares and assorted bits and pieces to exceed $2000 or more.
I'm going to put together a buget for costs. but you also need to consider TIME is MONEY as well, and saving you 2-3 hours in a good size match is worth how much? also the costs call depend on a LOT of factors.. eg if you have a computer at the club, and a member with a smart phone, then your start up costs (for an L1 - L2) is NOTHING.
Durability - I dont think PDAs will hold up to the abuse that they might be exposed to on a shooting range, dust, the elements, user neglect, and such I think would cause these devices to fail fairly quickly. Also, what would happen if a PDA being used on a range has been dropped and damaged/broke/unable to power back on before its been synced with the master pc running MSS? Without scoresheets that means all the shooters would need to reshoot the stage as their data was lost.
Again a very valid concern, and this can be mitigated two ways..
1) is you use the storage card for all "intrim" scores, then you can just take the SDIO card out, and take it to another PDA or to the computer, and no data (that was already scored) is lost. also depending on if you want to use Wifi, then your scores can be sent IMMEDIATLY to the PC in the club house after you have signed it.. no need to "collect" The data on the PDA.
the abuse concern is very valid as well, and different manufactures are better then others. the more you want to spend, the better they tend to be. (abuse wise)
Just my thoughts, my 2cents worth and some points that I am sure you have already considered.
Everyones 2 cents are very welcome and valid (or I would not ahve asked everyone for input in the first place.) the more things that are brought up for consideration, the better the solution will be..