How to create MS Paint clone with Python and pygame

Why not do both?

Draw a circle at each endpoint and a line between the two.

EDIT rofl, just couldn't stop myself.

Actually, you don't want to use pygame.draw.line because it cheats. It fills a 1 pixel wide row or column (depending on angle of attack) of pixels. If you do go at a roughly perpendicular angle, 0 deg or 90 deg, this isn't an issue, but at 45's, you'll notice a sort of string bean effect.

The only solution is to draw a circle at every pixel's distance. Here...

import pygame, random

screen = pygame.display.set_mode((800,600))

draw_on = False
last_pos = (0, 0)
color = (255, 128, 0)
radius = 10

def roundline(srf, color, start, end, radius=1):
    dx = end[0]-start[0]
    dy = end[1]-start[1]
    distance = max(abs(dx), abs(dy))
    for i in range(distance):
        x = int( start[0]+float(i)/distance*dx)
        y = int( start[1]+float(i)/distance*dy)
        pygame.draw.circle(srf, color, (x, y), radius)

try:
    while True:
        e = pygame.event.wait()
        if e.type == pygame.QUIT:
            raise StopIteration
        if e.type == pygame.MOUSEBUTTONDOWN:
            color = (random.randrange(256), random.randrange(256), random.randrange(256))
            pygame.draw.circle(screen, color, e.pos, radius)
            draw_on = True
        if e.type == pygame.MOUSEBUTTONUP:
            draw_on = False
        if e.type == pygame.MOUSEMOTION:
            if draw_on:
                pygame.draw.circle(screen, color, e.pos, radius)
                roundline(screen, color, e.pos, last_pos,  radius)
            last_pos = e.pos
        pygame.display.flip()

except StopIteration:
    pass

pygame.quit()

Not blitting at each loop step can improve the speed of the drawing (using this code adapted from the previous one allow to remove lag problem on my machine)

import pygame, random

screen = pygame.display.set_mode((800,600))

draw_on = False
last_pos = (0, 0)
color = (255, 128, 0)
radius = 10

def roundline(srf, color, start, end, radius=1):
    dx = end[0]-start[0]
    dy = end[1]-start[1]
    distance = max(abs(dx), abs(dy))
    for i in range(distance):
        x = int( start[0]+float(i)/distance*dx)
        y = int( start[1]+float(i)/distance*dy)
        pygame.display.update(pygame.draw.circle(srf, color, (x, y), radius))

try:
    while True:
        e = pygame.event.wait()
        if e.type == pygame.QUIT:
            raise StopIteration
        if e.type == pygame.MOUSEBUTTONDOWN:
            color = (random.randrange(256), random.randrange(256), random.randrange(256))
            pygame.draw.circle(screen, color, e.pos, radius)
            draw_on = True
        if e.type == pygame.MOUSEBUTTONUP:
            draw_on = False
        if e.type == pygame.MOUSEMOTION:
            if draw_on:
                pygame.display.update(pygame.draw.circle(screen, color, e.pos, radius))
                roundline(screen, color, e.pos, last_pos,  radius)
            last_pos = e.pos
        #pygame.display.flip()

except StopIteration:
    pass

pygame.quit()

For the first problem, you need have a background, even if its just a color. I had the same problem with a replica pong game i made. Here is an example of a replica paint program I made, left click to draw, right click to erase, click on the color image to choose a color, and up button to clear screen:

import os
os.environ['SDL_VIDEO_CENTERED'] = '1'
from pygamehelper import *
from pygame import *
from pygame.locals import *
from vec2d import *
from math import e, pi, cos, sin, sqrt
from random import uniform

class Starter(PygameHelper):
    def __init__(self):
        self.w, self.h = 800, 600
        PygameHelper.__init__(self, size=(self.w, self.h), fill=((255,255,255)))

        self.img= pygame.image.load("colors.png")
        self.screen.blit(self.img, (0,0))

        self.drawcolor= (0,0,0)
        self.x= 0

    def update(self):
        pass

    def keyUp(self, key):
        if key==K_UP:
            self.screen.fill((255,255,255))
            self.screen.blit(self.img, (0,0))




    def mouseUp(self, button, pos):
        pass

    def mouseMotion(self, buttons, pos, rel):
        if pos[1]>=172: 
            if buttons[0]==1:
                #pygame.draw.circle(self.screen, (0,0,0), pos, 5)
                pygame.draw.line(self.screen, self.drawcolor, pos, (pos[0]-rel[0], pos[1]-rel[1]),5)                
            if buttons[2]==1:
                pygame.draw.circle(self.screen, (255,255,255), pos, 30)
            if buttons[1]==1:
                #RAINBOW MODE
                color= self.screen.get_at((self.x, 0))
                pygame.draw.line(self.screen, color, pos, (pos[0]-rel[0], pos[1]-rel[1]), 5)

                self.x+= 1
                if self.x>172: self.x=0

        else:
            if pos[0]<172:
                if buttons[0]==1:
                    self.drawcolor= self.screen.get_at(pos)
                    pygame.draw.circle(self.screen, self.drawcolor, (250, 100), 30)

    def draw(self):
        pass
        #self.screen.fill((255,255,255))
        #pygame.draw.circle(self.screen, (0,0,0), (50,100), 20)

s = Starter()
s.mainLoop(40)