Here are the mistakes Steve comments about:

1- Try to avoid run-on sentences.
In many languages people can make very long sentences naturally, chaining subordinate clauses non-stop. But that sounds horrible in English. English people prefer short sentences, usually never more than 3 sentences combined together, and better still just 2 or 1. Run-on sentences are not incorrect, but they look clumsy and sometimes difficult to understand for natives, who are not used to processing such long sentences.

WRONG
I saw a girl at the supermarket who looked just like my mother because she was someone who had the same kind of hairstyle that my mother just got done at the hairdresser's and I think she looks great that way.

RIGHT (an possible rephrasing)
I saw a girl at the supermarket who looked just like my mother. She looked the same because she had the same kind of hairstyle my mother just got done at the hairdresser's. By the way, I think my mother looks great like that.

(another rephrasing)
I saw a girl at the supermarket. She looked just like my mother because she had the same hairstyle. My mother had just got it done at the hairdresser's and I think she looks great that way.

2- Say vs Tell
They both mean the same but use different constructions:
SAY + thing said = I said hello to Richard and he said 'goodbye'
TELL + person = I told Richard hello
We can also use SAY with a person, but we need the preposition (this construction is correct but less elegant):
SAY + TO + person = She said to me all the things that she wanted to have

3- Mid-position (for adverbs, etc)
Frequency adverbs (and a some other grammatical words) go in mid-position. Mid position is different depending on the nature of the verb:
SPECIAL VERBS (modals and auxiliaries): Subject + s. verb + ***
- She can never be here on time
- You must quickly phone her
If we have more than one auxiliary in the sentence it's the same, it still goes after the first one:
Subject + s.verb + *** (+ s. verb + n. verb...)
- I am always doing extra work in the office
- They will probably be here on time.
- I'll always love you
(notice that special verbs are usually contracted in conversation, and if we placed something between the subject and the verb, we could not contract it)
NORMAL VERBS (the rest): Subject + *** + n. verb
- I never work on Sundays
- She also likes it
So the general rule of thumb should be: The mid-position is "BEFORE NORMAL VERBS AND AFTER SPECIAL VERBS"

Note: Special verbs are= to be, have, do, will-would, can-could, may-might, shall-should, must, ought to  (the rest of verbs are normal verbls)

4- Types of connectors and its punctuation
Here we have to make a distinction between two different kinds of connectors:
conjunctions and free connectors.

CONJUNCTIONS
Conjunctions join to simple sentences into one compound sentence, so we can't put a stop between them because it's only one sentence:
1- I like you. +  2- You are so nice (that's the reason) = I like you because you are so nice.
- This is cheap but too ugly
- It's late so we can't go there now
But if we start with the conjunction, then we need a comma separating both parts of the compound sentence (some prepositions can't start a sentence):
- I'll go with you if you pick me up = If you pick me up, I'll go with you
- I saw her when she entered the shop = When she entered the shop, I saw her

This is a grammar rule, but natives often do it wrong and are not consistent with the use of the comma. Nevertheless, natives can make mistakes that foreign student's just can't, so try to do it correctly, especially if you are sitting for an exam.

FREE CONNECTORS
Free connectors join two sentences in meaning, but not in structure. Both sentences remain different and separate, but we put the free connector between both of them to establish a relationship, and we separate the free connector from both sentences, usually using a stop before and a comma after it:
1- It's nice   2- I don't like it
- It's nice but I don't like it = It's nice. Nevertheless, I don't like it
These two sentences mean exactly the same (a contrast), but the first one is one compound sentence using a conjunction (BUT) and the second one is two single sentences related with a free connector (NEVERTHELESS). The free connector is not part of any of the sentences (it's a free element), so it is separated from both with a stop and a comma (----- . Nevertheless,  -----).

1- I was painting the walls   2- Susan was cleaning the windows
- I was painting the walls while Susan was cleaning the windows (conjunction: WHILE)
- While I was painting the walls, Susan was cleaning the windows (reversed order with a comma)
- I was painting the walls. Meanwhile, Susan was cleaning the windows (free connector, two separate sentences)

Note: full stop (BrE) = period (AmE)
A major no-no = A thing you should never do (major = very important)