I tried some digital scales about 20 years ago but they had an auto power off feature (to save battery life) which meant that if you put some stuff on the scales and then left it unattended for more than the auto shut off time (7 minutes?), which I found I did several times the first time I used it, it would turn off AND forget the weight so I'd have to tip the grains/hops out and re-weigh them. It was extra effort and inconvenience so I returned it to the shop and changed it for one of those old-fashioned ones with a pan for adding weights. No batteries, no problems and I've used it ever since. Also I found that my scales can easily weigh down to 1/4 oz but this was at the limit of resolution of digital scales. Having said that, there may be better ditital scales out there these days that don't suffer from the shortcomings I encountered.
Regarding thermometers, I agree 100% with the comments about mercury thermometers with the additional comment that not only will a broken thermometer contaminate your current brew but it will also contaminate the equipment the breakage occurred in. Losing a brew is bad enough, but losing a boiler or mash tun would be a tragedy!
As an aside, if you've ever read the small print of what is barred from aeroplanes you'll find that mercury thermometers are included. Apparently the reason is that if one broke on a plane it would penetrate into the structure of the plane weakening the metal and they'd have no choice but to scrap the plane. If they found out that it was you that did it they'd sue you for the cost of a replacement plane! Another reason to avoid mercury?
Glass/alcohol thermometers are safe and probably the most accurate although the response is a bit slow and you need to make sure you have a 76mm (usually) immersion rather than a full immersion one (used for measuring room temperature etc.) which will only be accurate if you drop the entire thermometer into your brew which makes reading the temperature a bit tricky. <!-- s:wink: --><img src="{SMILIES_PATH}/icon_wink.gif" alt="

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Digital thermometers are faster than glass but probably not quite as accurate, although probably good enough for brewing. I now use a digital thermometer for 95%+ of my brewing and only use the glass one if I want to double check for some reason (usually mash temperature). Mine is probably accurate to about 1 degC.
I also have a "laser guided" thermometer that works by measuring infra-red radiation. I'd suggest that you don't waste your money buying one of these toys. It is very fast (instant) but horribly innacurate and is confused by bubbles on the liquid surface as well as steam coming from that surface so it consistently reads 10-20 degF low for brewing liquids. If you are aware of this shortcoming and apply some sort of mental correction to its readings then it can give a very rough idea of temperature. I tend to use mine while bringing to the boil and cooling the wort down, but I could happily live without it.