Hmmm ... there is so much misunderstanding in Gordon's post that it's difficult to know where to start.
Planck was looking at black body radiation. In order to get an equation that described the observed frequency spectrum, he made the assumption that energy could only be exchanged in amounts proportional to the frequency. This does not imply the existence of photons - something he opposed all his life. He certainly did not say that material objects are made of lumpy bits of energy. Mass/energy equivalence had to wait for Einstein't theory of relativity.
Time is not quantised. In all theories that work, it is continuous. If it were not continuous, you would not be able to differentiate with respect to it, and you would be unable to do any useful calculations.
The continuous spectrum is a bit odd. When you observe a continuous spectrum (e.g. black body radiation) for a given period of time, what you have observed is a finite (but very large!) number of photons, each with a specific energy. Planck's equation for black body radiation only tells us what proportion of the photons will be in a given energy range. It's a differential equation showing the derivative of the proportion with respect to the width of the range as the range tends to zero. When we plot a theoretical energy distribution as a continuous graph, we are plotting how that derivative varies as a function of energy. When we plot an observed spectrum as a line, we are merely joining up the closely-spaced dots. The spacing is determined by how much resolution our instrument has.
Now the Plank mass/length/time etc. These have absolutely no physical significance. They are units in just the same sense that the year, second, yard, metre, kilogram, ounce etc etc etc are units. Obviously, we can pick any units we want - the inch and the metre are completely arbitrary. The constants of nature will take different values in different units - e.g. the speed of light is 300,000,000 metres per second or 186,000 miles per second or 1 light-year per year or some silly number of furlongs per fortnight. What are these Planck units then? They are the units that result in the constants of nature that keep cluttering up our equations having the numerical value of 1.
The Planck mass certainly isn't the smallest mass there can be - obviously not, as it's the size of a grain of dust, and we know atoms are a lot less massive than that.